TSTP Solution File: SWV675-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV675-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:27:42 EDT 2022
% Result : Unsatisfiable 23.37s 23.72s
% Output : Refutation 23.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SWV675-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Wed Jun 15 11:36:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.05/1.45 *** allocated 10000 integers for termspace/termends
% 1.05/1.45 *** allocated 10000 integers for clauses
% 1.05/1.45 *** allocated 10000 integers for justifications
% 1.05/1.45 *** allocated 15000 integers for termspace/termends
% 1.05/1.45 *** allocated 22500 integers for termspace/termends
% 1.05/1.45 *** allocated 33750 integers for termspace/termends
% 1.05/1.45 Bliksem 1.12
% 1.05/1.45
% 1.05/1.45
% 1.05/1.45 Automatic Strategy Selection
% 1.05/1.45
% 1.05/1.45 Clauses:
% 1.05/1.45 [
% 1.05/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 1.05/1.45 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.05/1.45 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.05/1.45 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 1.05/1.45 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.05/1.45 'tc_nat' ), 'tc_nat' ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 1.05/1.45 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 1.05/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.45 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) )
% 1.05/1.45 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.05/1.45 , 'tc_nat' ) ) ],
% 1.05/1.45 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.05/1.45 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.05/1.45 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 1.05/1.45 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.45 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 1.05/1.45 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.45 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.05/1.45 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 1.05/1.45 , Z, 'tc_nat' ) ) ],
% 1.05/1.45 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.05/1.45 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.05/1.45 , Z, 'tc_nat' ) ) ],
% 1.05/1.45 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 1.05/1.45 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.45 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 1.05/1.45 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.45 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 1.05/1.45 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.45 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 1.05/1.45 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.05/1.45 ), =( Z, Y ) ],
% 1.05/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.05/1.45 ) ],
% 1.05/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.05/1.45 ) ],
% 1.05/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.05/1.45 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.05/1.45 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.05/1.45 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.05/1.45 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.05/1.45 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.05/1.45 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.05/1.45 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.05/1.45 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.05/1.45 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.05/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.45 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.05/1.45 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 1.05/1.45 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.05/1.45 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.05/1.45 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.05/1.45 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 1.05/1.45 ,
% 1.05/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.45 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.05/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.05/1.45 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.05/1.45 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.05/1.45 , Y, X ) ) ],
% 1.05/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.05/1.45 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.05/1.45 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 1.05/1.45 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ],
% 1.05/1.45 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.05/1.45 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.45 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.05/1.45 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.05/1.45 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.45 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.05/1.45 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.05/1.45 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.05/1.45 ,
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.05/1.45 ,
% 1.05/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.05/1.45 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.45 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.05/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.05/1.45 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 1.05/1.45 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.05/1.45 'tc_nat' ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.05/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.05/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.05/1.45 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.05/1.45 'c_GCD_Ogcd__class_Ogcd'( Y, 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 1.05/1.45 ), 'tc_nat' ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 1.05/1.45 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.05/1.45 ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.05/1.45 ), =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.45 Y, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ),
% 1.05/1.45 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.45 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.05/1.45 , T, X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.05/1.45 , T, X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.05/1.45 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.05/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.05/1.45 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.05/1.45 ,
% 1.05/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.05/1.45 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.05/1.45 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.05/1.45 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.05/1.45 ],
% 1.05/1.45 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.05/1.45 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.05/1.45 ],
% 1.05/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 1.05/1.45 Y, 'tc_nat' ) ) ],
% 1.05/1.45 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.05/1.45 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.05/1.45 ],
% 1.05/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.05/1.45 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.05/1.45 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.05/1.45 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.05/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 1.05/1.45 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_Suc'( X ), 'tc_nat' ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), 'c_Fact_Ofact__class_Ofact'(
% 1.05/1.45 X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.05/1.45 X ) ],
% 1.05/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.05/1.45 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.05/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.05/1.45 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.45 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.05/1.45 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.05/1.45 ,
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.05/1.45 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.05/1.45 ,
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.05/1.45 , X ), Z, X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.05/1.45 , X ), Z, X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.05/1.45 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.05/1.45 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.05/1.45 , Y, X ) ) ],
% 1.05/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 1.05/1.45 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 1.05/1.45 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 1.05/1.45 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.05/1.45 , Z, 'tc_nat' ) ) ],
% 1.05/1.45 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.05/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.05/1.45 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.05/1.45 ],
% 1.05/1.45 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.05/1.45 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 1.05/1.45 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.45 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.45 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.05/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.45 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.05/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.45 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.45 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.05/1.45 ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.05/1.45 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.45 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.05/1.45 , Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.45 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.45 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.45 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.45 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.45 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.45 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.05/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.45 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.45 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.45 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.05/1.45 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.45 'tc_nat' ), 'c_Power_Opower__class_Opower'( Y, X, 'tc_nat' ), 'tc_nat' )
% 1.05/1.45 ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.05/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.05/1.45 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.05/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.05/1.45 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Power_Opower__class_Opower'( Y
% 1.05/1.45 , 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ), 'tc_nat'
% 1.05/1.45 ) ],
% 1.05/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.05/1.45 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 1.05/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.05/1.45 ) ) ],
% 1.05/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.45 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.05/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.05/1.45 ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.05/1.45 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.45 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 1.05/1.45 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.05/1.45 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.05/1.45 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.05/1.45 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.05/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 1.05/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Fact_Ofact__class_Ofact'( Y,
% 1.05/1.45 'tc_nat' ), X ), X ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.05/1.45 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.05/1.45 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.45 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.05/1.45 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.05/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.05/1.45 T, X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.05/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.05/1.45 X ), Z, X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.05/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.05/1.45 T, X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.05/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.05/1.45 X ), T, X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.05/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.05/1.45 T, X ), X ) ) ],
% 1.05/1.45 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.05/1.45 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.05/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.05/1.45 X ), T, X ) ) ],
% 1.05/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.05/1.45 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.05/1.45 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.05/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.05/1.45 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.05/1.46 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.05/1.46 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.05/1.46 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.05/1.46 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.05/1.46 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.05/1.46 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.05/1.46 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.46 'c_Power_Opower__class_Opower'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.05/1.46 , 'tc_nat' ), 'tc_nat' ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.05/1.46 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 1.05/1.46 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.05/1.46 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.05/1.46 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.05/1.46 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 1.05/1.46 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.05/1.46 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.05/1.46 Y, 'tc_nat' ), 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.05/1.46 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.05/1.46 Y, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.05/1.46 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.05/1.46 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ) ],
% 1.05/1.46 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.05/1.46 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.05/1.46 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.05/1.46 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 1.05/1.46 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.05/1.46 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.05/1.46 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.05/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.05/1.46 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.05/1.46 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 1.05/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 1.05/1.46 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 1.05/1.46 X ), X ) ) ],
% 1.05/1.46 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Power_Opower__class_Opower'( X
% 1.05/1.46 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 1.05/1.46 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 1.05/1.46 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 1.05/1.46 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.05/1.46 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.46 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.05/1.46 X ) ) ), =( Z, T ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.05/1.46 X ) ) ), =( Z, T ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.05/1.46 X ) ) ), =( Y, T ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.46 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.46 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.05/1.46 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.46 X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.05/1.46 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.05/1.46 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.05/1.46 ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.05/1.46 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.05/1.46 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.05/1.46 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.05/1.46 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.05/1.46 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 1.05/1.46 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.05/1.46 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.05/1.46 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.05/1.46 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 1.05/1.46 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.05/1.46 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), 'tc_nat' ),
% 1.05/1.46 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 1.05/1.46 , X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.05/1.46 , Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.05/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.05/1.46 ), X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.05/1.46 ), X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.05/1.46 ), X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.05/1.46 ), X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.05/1.46 , Y, X ), X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.05/1.46 , Z, X ), X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.05/1.46 , Z, X ), X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.46 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.05/1.46 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.46 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.05/1.46 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.05/1.46 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.05/1.46 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.05/1.46 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.05/1.46 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.05/1.46 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.05/1.46 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.05/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T
% 1.05/1.46 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.05/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T
% 1.05/1.46 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Oinverse__class_Oinverse'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.05/1.46 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), X ), X ), X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.05/1.46 , Y, X ) ) ],
% 1.05/1.46 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.05/1.46 , Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.05/1.46 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.05/1.46 , T, X ), X ), T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.05/1.46 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.05/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , 'tc_nat' ), 'tc_nat' ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.05/1.46 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.05/1.46 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.05/1.46 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.05/1.46 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.05/1.46 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.05/1.46 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.05/1.46 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.05/1.46 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.05/1.46 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.05/1.46 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.46 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 1.05/1.46 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.05/1.46 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.05/1.46 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.05/1.46 Y, T, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.05/1.46 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.05/1.46 Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X )
% 1.05/1.46 , 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.05/1.46 'c_Power_Opower__class_Opower'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.05/1.46 X ), Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.05/1.46 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat'
% 1.05/1.46 ), 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X
% 1.05/1.46 ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.05/1.46 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.05/1.46 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.05/1.46 X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z
% 1.05/1.46 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.05/1.46 , T, X ), X ) ) ],
% 1.05/1.46 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ) ), =( Y, Z ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.46 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.05/1.46 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.05/1.46 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.05/1.46 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_Power_Opower__class_Opower'( X, Y,
% 1.05/1.46 'tc_nat' ), 'c_Power_Opower__class_Opower'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.05/1.46 , 'c_Power_Opower__class_Opower'( 'c_GCD_Ogcd__class_Ogcd'( X, Z,
% 1.05/1.46 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.05/1.46 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.05/1.46 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 1.05/1.46 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 1.05/1.46 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.05/1.46 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.05/1.46 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.05/1.46 , Y, X ) ) ],
% 1.05/1.46 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.05/1.46 'tc_nat' ), Y, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.05/1.46 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 1.05/1.46 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.05/1.46 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 1.05/1.46 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.05/1.46 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.46 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 1.05/1.46 ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.46 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 1.05/1.46 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 1.05/1.46 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 1.05/1.46 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.05/1.46 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.05/1.46 , 'c_Power_Opower__class_Opower'( Y, Z, X ) ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.05/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.46 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.05/1.46 ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.46 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.05/1.46 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 T, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.05/1.46 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 1.05/1.46 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.05/1.46 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.05/1.46 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.05/1.46 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.46 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.05/1.46 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.05/1.46 ) ],
% 1.05/1.46 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.05/1.46 'tc_nat' ), Z, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z
% 1.05/1.46 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.46 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.05/1.46 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( X
% 1.05/1.46 , Z, 'tc_nat' ), 'c_Power_Opower__class_Opower'( Y, Z, 'tc_nat' ),
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'(
% 1.05/1.46 X, Y, 'tc_nat' ), 'c_Power_Opower__class_Opower'( Z, Y, 'tc_nat' ),
% 1.05/1.46 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) )
% 1.05/1.46 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( X
% 1.05/1.46 , Z, 'tc_nat' ), 'c_Power_Opower__class_Opower'( Y, Z, 'tc_nat' ),
% 1.05/1.46 'tc_nat' ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.05/1.46 ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T
% 1.05/1.46 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.05/1.46 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.05/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.05/1.46 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.05/1.46 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.05/1.46 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Power_Opower__class_Opower'( Y,
% 1.05/1.46 Z, 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 1.05/1.46 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.05/1.46 ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.05/1.46 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.05/1.46 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.05/1.46 ), X ), X ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.05/1.46 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.05/1.46 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 1.05/1.46 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, X, 'tc_nat' ), X ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.46 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.05/1.46 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.05/1.46 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.05/1.46 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.05/1.46 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.05/1.46 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.05/1.46 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.05/1.46 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.05/1.46 , X ), W, X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.46 X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.05/1.46 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.05/1.46 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.05/1.46 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.05/1.46 ), X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.46 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.05/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.05/1.46 ), X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.05/1.46 X ) ) ],
% 1.05/1.46 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 X, T, 'tc_nat' ) ],
% 1.05/1.46 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.05/1.46 X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.05/1.46 X ) ) ],
% 1.05/1.46 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_Power_Opower__class_Opower'( X, Y
% 1.05/1.46 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.05/1.46 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.05/1.46 , T, X ), X ), T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.05/1.46 , T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), T, X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.05/1.46 , T, X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.05/1.46 , T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.05/1.46 , T, X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.05/1.46 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 1.05/1.46 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 1.05/1.46 W, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.05/1.46 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.05/1.46 , X ), T, X ), W, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 1.05/1.46 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 1.05/1.46 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 1.05/1.46 W, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.05/1.46 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.05/1.46 , X ), W, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.05/1.46 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 1.05/1.46 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 1.05/1.46 Z, X ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.46 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.05/1.46 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.05/1.46 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.05/1.46 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.05/1.46 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), Y,
% 1.05/1.46 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.05/1.46 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.05/1.46 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.05/1.46 , T ), =( X, Z ) ],
% 1.05/1.46 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.05/1.46 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.05/1.46 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.05/1.46 , T ), =( X, Z ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.46 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.05/1.46 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.46 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.05/1.46 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.46 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'tc_nat' ), =( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.46 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'tc_nat' ), =( X,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.05/1.46 , X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.05/1.46 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.05/1.46 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( Y,
% 1.05/1.46 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat'
% 1.05/1.46 ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 1.05/1.46 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat'
% 1.05/1.46 ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 1.05/1.46 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.05/1.46 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 1.05/1.46 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 1.05/1.46 X ), Z, X ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Power_Opower__class_Opower'( X
% 1.05/1.46 , 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ), 'tc_nat'
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.46 'c_Power_Opower__class_Opower'( X, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.05/1.46 , 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 1.05/1.46 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 1.05/1.46 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.05/1.46 X ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 1.05/1.46 , X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.05/1.46 ), X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 Y, X, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.05/1.46 , Y, 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.05/1.46 X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.05/1.46 Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.05/1.46 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.05/1.46 ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.05/1.46 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.05/1.46 , X ) ) ],
% 1.05/1.46 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.05/1.46 , Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.05/1.46 , Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), X ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.05/1.46 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.05/1.46 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.05/1.46 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.05/1.46 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.05/1.46 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.05/1.46 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.05/1.46 , Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 1.05/1.46 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.05/1.46 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.05/1.46 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( T,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, U, 'tc_nat' ), 'tc_nat' ) ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.05/1.46 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.46 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.05/1.46 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.05/1.46 Y, T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 1.05/1.46 ), Y, X ) ), =( Z, T ) ],
% 1.05/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.05/1.46 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.05/1.46 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.05/1.46 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.46 X ), T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.05/1.46 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.05/1.46 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.05/1.46 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.05/1.46 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.05/1.46 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.05/1.46 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.05/1.46 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.05/1.46 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.05/1.46 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.05/1.46 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.05/1.46 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.05/1.46 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.05/1.46 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Z, X, 'tc_nat'
% 1.05/1.46 ), 'c_Power_Opower__class_Opower'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.05/1.46 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Fact_Ofact__class_Ofact'( Y,
% 1.05/1.46 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.05/1.46 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), Y,
% 1.05/1.46 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.05/1.46 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.05/1.46 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.05/1.46 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.05/1.46 ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.05/1.46 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.05/1.46 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 1.05/1.46 Y, Z, 'tc_nat' ), 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.05/1.46 , Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat'
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 1.05/1.46 Y, Z, 'tc_nat' ), 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.05/1.46 , Y, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.05/1.46 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.05/1.46 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.05/1.46 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.05/1.46 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.05/1.46 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.05/1.46 , 'tc_nat' ), X, 'tc_nat' ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.05/1.46 , 'tc_nat' ), X, 'tc_nat' ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.05/1.46 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.05/1.46 , 'tc_nat' ), X, 'tc_nat' ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.05/1.46 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.05/1.46 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.05/1.46 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.05/1.46 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.05/1.46 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.05/1.46 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.05/1.46 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.05/1.46 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.05/1.46 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.05/1.46 , Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.05/1.46 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.05/1.46 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.05/1.46 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.46 , X ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.46 ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.05/1.46 ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.05/1.46 , X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.46 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.46 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.46 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.05/1.46 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.46 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.05/1.46 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.05/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.05/1.46 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 1.05/1.46 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.05/1.46 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.05/1.46 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~( 'c_lessequals'( Z,
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), X ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.05/1.46 , T, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.05/1.46 , Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.05/1.46 , T, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.05/1.46 , Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.05/1.46 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.05/1.46 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.46 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.05/1.46 , T, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.05/1.46 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.05/1.46 , Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.05/1.46 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.05/1.46 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.05/1.46 ), =( 'c_Divides_Odiv__class_Omod'( 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.46 Y, X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.46 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.05/1.46 ), ~( =( 'c_Divides_Odiv__class_Omod'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.46 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , 'tc_nat' ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , 'tc_nat' ), 'tc_nat' ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' )
% 1.05/1.46 , 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.05/1.46 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.46 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 1.05/1.46 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.05/1.46 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.05/1.46 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.05/1.46 X ), T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.05/1.46 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.05/1.46 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.05/1.46 X ), T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.05/1.46 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.05/1.46 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.05/1.46 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.05/1.46 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.05/1.46 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.05/1.46 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.05/1.46 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.05/1.46 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.05/1.46 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.05/1.46 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.05/1.46 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.05/1.46 X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.05/1.46 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 Z, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 Z, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.05/1.46 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.05/1.46 X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.05/1.46 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 Y, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 Y, T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.05/1.46 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ =( 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.05/1.46 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.05/1.46 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.05/1.46 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.05/1.46 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ],
% 1.05/1.46 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.05/1.46 , Y, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.05/1.46 , T, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.05/1.46 , T, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.05/1.46 , Y, X ), X ) ) ],
% 1.05/1.46 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_GCD_Ogcd__class_Ogcd'( Y, 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 1.05/1.46 ), 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.05/1.46 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.05/1.46 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , 'tc_nat' ), X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.05/1.46 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.05/1.46 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , 'tc_nat' ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.05/1.46 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 1.05/1.46 ],
% 1.05/1.46 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'( X, Y,
% 1.05/1.46 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' )
% 1.05/1.46 , 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 1.05/1.46 , X ) ) ],
% 1.05/1.46 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.05/1.46 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 1.05/1.46 , X ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.05/1.46 , 'tc_nat' ), Z, 'tc_nat' ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X
% 1.05/1.46 , 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' )
% 1.05/1.46 ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.05/1.46 , 'tc_nat' ), Z, 'tc_nat' ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y
% 1.05/1.46 , 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' )
% 1.05/1.46 ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.05/1.46 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 1.05/1.46 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.05/1.46 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.05/1.46 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.05/1.46 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.05/1.46 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.05/1.46 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.05/1.46 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.05/1.46 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.05/1.46 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.05/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.05/1.46 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.05/1.46 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~(
% 1.05/1.46 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.46 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~(
% 1.05/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.05/1.46 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.05/1.46 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.05/1.46 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.46 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.05/1.46 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.46 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.05/1.46 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.05/1.46 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.05/1.46 ), X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.46 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.05/1.46 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.05/1.46 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.05/1.46 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.05/1.46 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.05/1.46 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.05/1.46 ), X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.05/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.05/1.46 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.05/1.46 ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.05/1.46 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.05/1.46 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.05/1.46 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.05/1.46 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.05/1.46 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.05/1.46 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.05/1.46 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.05/1.46 , X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.05/1.46 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.05/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.05/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.05/1.46 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.05/1.46 ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.05/1.46 ), X ), Z, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.05/1.46 ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.05/1.46 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.05/1.46 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =(
% 1.05/1.46 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Z,
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ), X ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), ~(
% 1.05/1.46 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.05/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.05/1.46 'tc_nat' ), X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.05/1.46 ,
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.05/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.05/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.05/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.05/1.46 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 1.05/1.46 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.05/1.46 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.46 X ), T, X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 1.05/1.46 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.05/1.46 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.05/1.46 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.46 X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.05/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.05/1.46 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.05/1.46 X ), X ) ) ],
% 1.05/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.05/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.05/1.46 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), X ), X ) ],
% 1.05/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.05/1.46 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.05/1.46 ) ) ],
% 1.05/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.05/1.46 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.09/1.46 ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 1.09/1.46 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.46 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.46 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.09/1.46 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.46 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.46 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.09/1.46 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.46 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.46 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.46 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.46 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.09/1.46 ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.46 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.09/1.46 X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.46 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.09/1.46 ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.46 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.09/1.46 X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.09/1.46 ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.09/1.46 ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.09/1.46 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.09/1.46 , X ), Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.46 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.09/1.46 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.09/1.46 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.46 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.09/1.46 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.09/1.46 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.09/1.46 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.09/1.46 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.09/1.46 ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.46 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.09/1.46 , X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.09/1.46 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.46 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.09/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.46 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.09/1.46 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.46 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'( Z,
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.09/1.46 , X ), X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.46 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 Y, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), T, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.09/1.46 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.09/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.46 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.09/1.46 ), X ), Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.46 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.09/1.46 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.46 X ), T, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.09/1.46 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.09/1.46 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.09/1.46 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.09/1.46 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.09/1.46 ), X ), Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.46 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.09/1.46 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.46 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.09/1.46 ), X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.46 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.46 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 , X ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), T, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.46 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.09/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.46 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.09/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), T, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.09/1.46 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.09/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.46 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.09/1.46 ), X ), Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 Y, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), T, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.46 , X ), X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.46 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.09/1.46 ), X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.09/1.46 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.46 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.09/1.46 , X ), X ), Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), =( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.09/1.46 Z, 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Z, Y, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.09/1.46 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.09/1.46 ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.09/1.46 ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.09/1.46 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y,
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( T, X )
% 1.09/1.46 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.09/1.46 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.09/1.46 , Z, X ), Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.46 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.46 ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.46 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.46 ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.46 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.09/1.46 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.09/1.46 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.09/1.46 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.09/1.46 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ) ), =( Z,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.09/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.09/1.46 Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.09/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.09/1.46 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 , T, X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.09/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.09/1.46 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 , T, X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.09/1.46 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.09/1.46 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ),
% 1.09/1.46 ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X
% 1.09/1.46 ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.09/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.09/1.46 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.09/1.46 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 1.09/1.46 ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.09/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.09/1.46 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.09/1.46 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 , Z, X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.09/1.46 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.09/1.46 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 , Z, X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.09/1.46 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.09/1.46 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.09/1.46 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.09/1.46 , Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.09/1.46 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.09/1.46 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.09/1.46 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.09/1.46 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.46 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.09/1.46 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.09/1.46 ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.46 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.09/1.46 ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.09/1.46 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.46 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.46 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.46 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.46 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.46 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.09/1.46 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Fact_Ofact__class_Ofact'( Y,
% 1.09/1.46 'tc_nat' ), X ), X ), X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 1.09/1.46 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.46 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 1.09/1.46 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.46 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 1.09/1.46 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.46 Y, T, X ), X ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.09/1.46 , X ), X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.09/1.46 , X ), X ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.09/1.46 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.46 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.09/1.46 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.46 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 1.09/1.46 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.09/1.46 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.09/1.46 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.09/1.46 ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.09/1.46 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.46 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.09/1.46 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.09/1.46 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.09/1.46 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.09/1.46 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.09/1.46 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.09/1.46 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.09/1.46 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.09/1.46 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.09/1.46 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.09/1.46 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.09/1.46 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.09/1.46 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.09/1.46 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.09/1.46 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.09/1.46 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.09/1.46 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.09/1.46 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.09/1.46 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.09/1.46 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.09/1.46 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.09/1.46 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.46 X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.09/1.46 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.09/1.46 Y, X ), X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.09/1.46 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.46 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.46 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 , X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.46 ), ~( =( 'c_Power_Opower__class_Opower'( Y,
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.46 ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.46 ,
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.09/1.46 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.09/1.46 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.09/1.46 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.46 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.46 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.09/1.46 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.46 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.09/1.46 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.09/1.46 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.09/1.46 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.09/1.46 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.09/1.46 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.09/1.46 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.09/1.46 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.46 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.09/1.46 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.09/1.46 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.09/1.46 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.09/1.46 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.46 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.09/1.46 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.09/1.46 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.46 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.09/1.46 ) ],
% 1.09/1.46 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.46 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.46 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.09/1.46 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.46 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.46 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.09/1.47 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.09/1.47 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.09/1.47 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.09/1.47 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.09/1.47 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.09/1.47 , X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.09/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.09/1.47 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.09/1.47 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.09/1.47 , X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.09/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.09/1.47 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.09/1.47 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.09/1.47 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.09/1.47 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 1.09/1.47 , X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.47 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.09/1.47 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.09/1.47 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), T, X ) ), =( T,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.09/1.47 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), Z, X ) ), =( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.09/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.09/1.47 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 Y, T, X ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.09/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.09/1.47 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 Y, T, X ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.09/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.09/1.47 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.09/1.47 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.09/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.09/1.47 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.09/1.47 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.09/1.47 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.09/1.47 , T, X ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.09/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.09/1.47 X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ), T, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.09/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.09/1.47 Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.09/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.09/1.47 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.09/1.47 X ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.09/1.47 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.09/1.47 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.09/1.47 Z, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.09/1.47 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.09/1.47 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.09/1.47 Z, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.09/1.47 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.09/1.47 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.09/1.47 X ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.09/1.47 ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.09/1.47 ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.09/1.47 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.09/1.47 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.09/1.47 ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.09/1.47 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y
% 1.09/1.47 , Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X
% 1.09/1.47 ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.09/1.47 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, U,
% 1.09/1.47 X ), X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.09/1.47 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.09/1.47 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.09/1.47 , X ), W, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.09/1.47 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 1.09/1.47 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.09/1.47 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.09/1.47 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.09/1.47 , X ), T, X ), W, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 1.09/1.47 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.47 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.09/1.47 'c_HOL_Oabs__class_Oabs'( T, X ), X ) ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.09/1.47 'tc_nat' ), X ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.47 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.09/1.47 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.47 , 'tc_nat' ), X ), X ) ) ],
% 1.09/1.47 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.47 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), 'tc_nat' ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), 'tc_nat' ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.09/1.47 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.47 , 'tc_nat' ), X ) ],
% 1.09/1.47 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.09/1.47 , 'tc_nat' ), X ) ],
% 1.09/1.47 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.47 ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.47 ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.47 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.47 ), 'tc_nat' ), X ) ],
% 1.09/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.47 , X, 'tc_nat' ), X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 1.09/1.47 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.09/1.47 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.09/1.47 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.09/1.47 X ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.09/1.47 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.09/1.47 , T, X ), X ), T, X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.09/1.47 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.09/1.47 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.09/1.47 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.09/1.47 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.09/1.47 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 1.09/1.47 ), Y ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.09/1.47 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.09/1.47 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.09/1.47 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.09/1.47 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.09/1.47 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.09/1.47 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.09/1.47 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.09/1.47 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.09/1.47 , U, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.09/1.47 ), Y ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.09/1.47 Z, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.09/1.47 Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.09/1.47 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 1.09/1.47 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 1.09/1.47 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.09/1.47 , U, X ), X ), W, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Z, U, X ), W, X ), X ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, T, X ), W, X ), U, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 1.09/1.47 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.09/1.47 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 1.09/1.47 Y, Z, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.09/1.47 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.09/1.47 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.09/1.47 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.09/1.47 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.09/1.47 , T, X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 Z, T, 'tc_nat' ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.09/1.47 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.09/1.47 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.09/1.47 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.09/1.47 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.47 ) ), X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.09/1.47 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.47 ) ), X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.09/1.47 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.09/1.47 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat'
% 1.09/1.47 ), 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.09/1.47 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.09/1.47 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.09/1.47 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.09/1.47 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.09/1.47 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.09/1.47 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.09/1.47 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.09/1.47 X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X
% 1.09/1.47 ), X ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.09/1.47 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.09/1.47 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.47 T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.09/1.47 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.47 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.09/1.47 Y, X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.09/1.47 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 1.09/1.47 Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.47 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 , X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.09/1.47 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Z
% 1.09/1.47 , X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ), =( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.09/1.47 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.09/1.47 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.09/1.47 , X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.47 , 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.09/1.47 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.47 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.09/1.47 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.09/1.47 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( 'c_Power_Opower__class_Opower'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.09/1.47 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( 'c_Power_Opower__class_Opower'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), X, 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( 'c_Power_Opower__class_Opower'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), X, 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ) ) ],
% 1.09/1.47 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.09/1.47 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 1.09/1.47 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.47 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.47 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.09/1.47 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ), Y, X ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.09/1.47 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.47 X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.09/1.47 'c_Suc'( Z ), X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.09/1.47 Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.09/1.47 ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.09/1.47 Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y,
% 1.09/1.47 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.09/1.47 , Z, X ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.09/1.47 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.09/1.47 , Z, X ), 'c_Power_Opower__class_Opower'( T, U, X ), X ), ~(
% 1.09/1.47 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.09/1.47 , Z, X ), T, X ), ~( 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.09/1.47 , U, X ), T, X ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.09/1.47 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 1.09/1.47 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.47 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.47 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.09/1.47 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.09/1.47 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.47 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.09/1.47 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.09/1.47 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.09/1.47 , X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 Y, 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.09/1.47 Z, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'(
% 1.09/1.47 Z, X ), X ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 1.09/1.47 , 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.09/1.47 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ) ), 'tc_nat' ) )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.09/1.47 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 1.09/1.47 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.09/1.47 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.09/1.47 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.09/1.47 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 Y, T, X ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.09/1.47 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.09/1.47 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.09/1.47 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.09/1.47 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 1.09/1.47 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.09/1.47 'tc_nat' ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.09/1.47 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.09/1.47 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.09/1.47 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.09/1.47 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.09/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 1.09/1.47 ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.09/1.47 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.09/1.47 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ) ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ) ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ) ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 1.09/1.47 ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 1.09/1.47 ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.09/1.47 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.09/1.47 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 1.09/1.47 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.47 X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ) ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.09/1.47 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.09/1.47 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.09/1.47 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 1.09/1.47 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 1.09/1.47 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.09/1.47 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.09/1.47 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 1.09/1.47 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 1.09/1.47 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.09/1.47 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.09/1.47 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.09/1.47 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.09/1.47 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 1.09/1.47 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 1.09/1.47 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 1.09/1.47 'c_lessequals'( T, X, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 1.09/1.47 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U ) ],
% 1.09/1.47 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.09/1.47 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 1.09/1.47 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.09/1.47 ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.09/1.47 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.09/1.47 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.09/1.47 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.09/1.47 , 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat'
% 1.09/1.47 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.09/1.47 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.09/1.47 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.09/1.47 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.09/1.47 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.09/1.47 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.09/1.47 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.09/1.47 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.09/1.47 , X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.09/1.47 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.09/1.47 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.47 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ), ~(
% 1.09/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.47 , 'tc_nat' ), 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.47 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ), 'c_Power_Opower__class_Opower'( Y,
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.09/1.47 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ), X ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Z,
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z,
% 1.09/1.47 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 1.09/1.47 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.09/1.47 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), X, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ),
% 1.09/1.47 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), Y, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ),
% 1.09/1.47 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Z
% 1.09/1.47 , Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Y
% 1.09/1.47 , Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 1.09/1.47 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.09/1.47 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 1.09/1.47 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.09/1.47 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 1.09/1.47 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.47 Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 1.09/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.09/1.47 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 1.09/1.47 ), X, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.09/1.47 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.09/1.47 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 1.09/1.47 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.09/1.47 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.09/1.47 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.09/1.47 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.09/1.47 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.09/1.47 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.47 Z, T, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.09/1.47 Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z
% 1.09/1.47 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.09/1.47 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.47 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Z, Y, X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.09/1.47 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.09/1.47 ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.09/1.47 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~( 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.09/1.47 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.09/1.47 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.09/1.47 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.09/1.47 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.09/1.47 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.09/1.47 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.09/1.47 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.09/1.47 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.09/1.47 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.47 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.09/1.47 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.47 , X ), X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.09/1.47 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.09/1.47 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.09/1.47 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.47 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.09/1.47 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.09/1.47 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.09/1.47 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.09/1.47 X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.09/1.47 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.09/1.47 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.47 'c_lessequals'( Z, Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.09/1.47 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.47 'c_lessequals'( Z, Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.47 Y, T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.09/1.47 ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.09/1.47 , Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.09/1.47 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.09/1.47 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' )
% 1.09/1.47 ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.09/1.47 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.09/1.47 ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.09/1.47 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.09/1.47 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y,
% 1.09/1.47 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.09/1.47 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 1.09/1.47 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.09/1.47 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.09/1.47 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.09/1.47 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 1.09/1.47 , Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.09/1.47 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.09/1.47 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.09/1.47 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.47 T, Z, X ) ) ), =( Y, T ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.09/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.09/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.09/1.47 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.09/1.47 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.09/1.47 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.47 Y, T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.09/1.47 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.09/1.47 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.09/1.47 Z ), T, 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 1.09/1.47 'tc_nat' ), X ), Y, X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.09/1.47 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.47 Z, T, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.09/1.47 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.09/1.47 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.47 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.47 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 1.09/1.47 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.09/1.47 'c_lessequals'( Z, Y, X ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.47 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.09/1.47 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( T ), X ),
% 1.09/1.47 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.47 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.09/1.47 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.09/1.47 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.09/1.47 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.09/1.47 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.09/1.47 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 , X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.09/1.47 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 1.09/1.47 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.09/1.47 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.09/1.47 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.09/1.47 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.09/1.47 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.09/1.47 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.09/1.47 'tc_nat' ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.09/1.47 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.09/1.47 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.09/1.47 , X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.09/1.47 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.09/1.47 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.09/1.47 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.09/1.47 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 1.09/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.09/1.47 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.09/1.47 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.09/1.47 Y, X ), Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.09/1.47 ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.09/1.47 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.09/1.47 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.09/1.47 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.09/1.47 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.09/1.47 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.09/1.47 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.47 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.09/1.47 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.09/1.47 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.47 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ) ) ],
% 1.09/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.09/1.47 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.09/1.47 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.09/1.47 , Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.09/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.09/1.47 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.09/1.47 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.09/1.47 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.47 Z, T, X ), X ) ) ],
% 1.09/1.47 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( 't_a' ) ), ~( =( 'v_a',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.09/1.47 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.09/1.47 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.47 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.09/1.47 , X, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.09/1.47 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.09/1.47 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.09/1.47 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.09/1.47 ), X ), Y ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.47 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.09/1.47 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.09/1.47 ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 1.09/1.47 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.47 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.47 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.09/1.47 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.47 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.09/1.47 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.09/1.47 , T, X ) ) ), =( Z, T ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.09/1.47 , T, X ) ) ), =( Y, Z ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.47 ), X ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.47 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 1.09/1.47 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ), =( Y, Z ) ],
% 1.09/1.47 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 ) ), =( Y, Z ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.47 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 1.09/1.47 'tc_nat' ), X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.09/1.47 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.09/1.47 Y, T, X ), X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ), =( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.09/1.47 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.09/1.47 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.47 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.09/1.47 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.09/1.47 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.09/1.47 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.47 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.47 , X ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.09/1.47 ],
% 1.09/1.47 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 1.09/1.47 'tc_nat' ) ],
% 1.09/1.47 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 1.09/1.47 , X, 'tc_nat' ) ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ofield'( 't_a' ) ],
% 1.09/1.47 [ 'c_lessequals'( 'c_Suc'( 'v_y' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.47 ), 'tc_nat' ) ],
% 1.09/1.47 [ ~( =( 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.09/1.47 'v_a', 't_a' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.47 'tc_nat' ), 'c_Suc'( 'v_y' ), 'tc_nat' ), 't_a' ),
% 1.09/1.47 'c_HOL_Oinverse__class_Odivide'( 'c_Power_Opower__class_Opower'( 'v_a',
% 1.09/1.47 'c_Suc'( 'v_y' ), 't_a' ), 'c_Power_Opower__class_Opower'( 'v_a',
% 1.09/1.47 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 't_a' ), 't_a' ) ) ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Ono__zero__divisors'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_OrderedGroup_Oab__semigroup__mult'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_OrderedGroup_Oab__semigroup__add'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Odivision__ring'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Ocomm__semiring'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_OrderedGroup_Ocomm__monoid__add'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Ozero__neq__one'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Ocomm__ring__1'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Osemiring__1'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Osemiring__0'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_OrderedGroup_Oab__group__add'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Omult__zero'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Ocomm__ring'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_OrderedGroup_Omonoid__mult'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Osemiring'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_OrderedGroup_Omonoid__add'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_OrderedGroup_Ogroup__add'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Oring__1'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Oring'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Oidom'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.09/1.47 'class_Ring__and__Field_Odvd'( X ) ],
% 1.09/1.47 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), 'class_Power_Opower'( X ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.09/1.47 ],
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.09/1.47 ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.09/1.47 ],
% 1.09/1.47 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.09/1.47 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.09/1.47 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.09/1.47 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.09/1.47 ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.09/1.47 ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.09/1.47 ,
% 1.09/1.47 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.09/1.47 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.09/1.48 [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 1.09/1.48 [ 'class_Ring__and__Field_Odvd'( 'tc_Int_Oint' ) ],
% 1.09/1.48 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.09/1.48 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.09/1.48 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.09/1.48 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.09/1.48 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.09/1.48 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.09/1.48 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.09/1.48 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ]
% 1.09/1.48 ] .
% 1.09/1.48
% 1.09/1.48
% 1.09/1.48 percentage equality = 0.178430, percentage horn = 0.813131
% 1.09/1.48 This is a problem with some equality
% 1.09/1.48
% 1.09/1.48
% 1.09/1.48
% 1.09/1.48 Options Used:
% 1.09/1.48
% 1.09/1.48 useres = 1
% 1.09/1.48 useparamod = 1
% 1.09/1.48 useeqrefl = 1
% 1.09/1.48 useeqfact = 1
% 1.09/1.48 usefactor = 1
% 1.09/1.48 usesimpsplitting = 0
% 1.09/1.48 usesimpdemod = 5
% 1.09/1.48 usesimpres = 3
% 1.09/1.48
% 1.09/1.48 resimpinuse = 1000
% 1.09/1.48 resimpclauses = 20000
% 1.09/1.48 substype = eqrewr
% 1.09/1.48 backwardsubs = 1
% 1.09/1.48 selectoldest = 5
% 1.09/1.48
% 1.09/1.48 litorderings [0] = split
% 1.09/1.48 litorderings [1] = extend the termordering, first sorting on arguments
% 1.09/1.48
% 1.09/1.48 termordering = kbo
% 1.09/1.48
% 1.09/1.48 litapriori = 0
% 1.09/1.48 termapriori = 1
% 1.09/1.48 litaposteriori = 0
% 1.09/1.48 termaposteriori = 0
% 1.09/1.48 demodaposteriori = 0
% 1.09/1.48 ordereqreflfact = 0
% 1.09/1.48
% 1.09/1.48 litselect = negord
% 1.09/1.48
% 1.09/1.48 maxweight = 15
% 1.09/1.48 maxdepth = 30000
% 1.09/1.48 maxlength = 115
% 1.09/1.48 maxnrvars = 195
% 1.09/1.48 excuselevel = 1
% 1.09/1.48 increasemaxweight = 1
% 1.09/1.48
% 1.09/1.48 maxselected = 10000000
% 1.09/1.48 maxnrclauses = 10000000
% 1.09/1.48
% 1.09/1.48 showgenerated = 0
% 1.09/1.48 showkept = 0
% 1.09/1.48 showselected = 0
% 1.09/1.48 showdeleted = 0
% 1.09/1.48 showresimp = 1
% 1.09/1.48 showstatus = 2000
% 1.09/1.48
% 1.09/1.48 prologoutput = 1
% 1.09/1.48 nrgoals = 5000000
% 1.09/1.48 totalproof = 1
% 1.09/1.48
% 1.09/1.48 Symbols occurring in the translation:
% 1.09/1.48
% 1.09/1.48 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.09/1.48 . [1, 2] (w:1, o:129, a:1, s:1, b:0),
% 1.09/1.48 ! [4, 1] (w:0, o:55, a:1, s:1, b:0),
% 1.09/1.48 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.09/1.48 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.09/1.48 'tc_nat' [41, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.09/1.48 'c_HOL_Oord__class_Oless' [42, 3] (w:1, o:161, a:1, s:1, b:0),
% 1.09/1.48 'c_HOL_Otimes__class_Otimes' [44, 3] (w:1, o:162, a:1, s:1, b:0),
% 1.09/1.48 'class_Ring__and__Field_Oordered__idom' [46, 1] (w:1, o:63, a:1, s:1
% 1.09/1.48 , b:0),
% 1.09/1.48 'c_HOL_Oabs__class_Oabs' [49, 2] (w:1, o:154, a:1, s:1, b:0),
% 1.09/1.48 'class_Ring__and__Field_Oidom' [50, 1] (w:1, o:64, a:1, s:1, b:0),
% 1.09/1.48 'c_HOL_Ozero__class_Ozero' [51, 1] (w:1, o:65, a:1, s:1, b:0),
% 1.09/1.48 'c_Ring__and__Field_Odvd__class_Odvd' [52, 3] (w:1, o:163, a:1, s:1
% 1.09/1.48 , b:0),
% 1.09/1.48 'class_Ring__and__Field_Ocomm__semiring__1' [53, 1] (w:1, o:68, a:1
% 1.09/1.48 , s:1, b:0),
% 1.09/1.48 'c_GCD_Ogcd__class_Ogcd' [58, 3] (w:1, o:160, a:1, s:1, b:0),
% 1.09/1.48 'class_Orderings_Olinorder' [59, 1] (w:1, o:70, a:1, s:1, b:0),
% 1.09/1.48 'class_Ring__and__Field_Oordered__semidom' [60, 1] (w:1, o:72, a:1
% 1.09/1.48 , s:1, b:0),
% 1.09/1.48 'c_HOL_Oone__class_Oone' [61, 1] (w:1, o:73, a:1, s:1, b:0),
% 1.09/1.48 'c_Power_Opower__class_Opower' [62, 3] (w:1, o:164, a:1, s:1, b:0),
% 1.09/1.48 'class_OrderedGroup_Olordered__ab__group__add__abs' [63, 1] (w:1, o:
% 1.09/1.48 74, a:1, s:1, b:0),
% 1.09/1.48 'c_HOL_Oplus__class_Oplus' [64, 3] (w:1, o:165, a:1, s:1, b:0),
% 1.09/1.48 'c_lessequals' [65, 3] (w:1, o:166, a:1, s:1, b:0),
% 1.09/1.48 'c_Divides_Odiv__class_Omod' [66, 3] (w:1, o:167, a:1, s:1, b:0),
% 1.09/1.48 'class_Ring__and__Field_Oordered__ring__strict' [71, 1] (w:1, o:71
% 1.09/1.48 , a:1, s:1, b:0),
% 1.09/1.48 'c_Suc' [72, 1] (w:1, o:75, a:1, s:1, b:0),
% 1.09/1.48 'class_Ring__and__Field_Oordered__semiring__strict' [73, 1] (w:1, o:
% 1.09/1.48 76, a:1, s:1, b:0),
% 1.09/1.48 'class_OrderedGroup_Olordered__ab__group__add' [74, 1] (w:1, o:77, a:
% 1.09/1.48 1, s:1, b:0),
% 1.09/1.48 'class_Nat_Osemiring__char__0' [77, 1] (w:1, o:69, a:1, s:1, b:0),
% 1.09/1.48 'c_Nat_Osemiring__1__class_Oof__nat' [78, 2] (w:1, o:155, a:1, s:1
% 1.09/1.48 , b:0),
% 1.09/1.48 'class_Ring__and__Field_Oring' [79, 1] (w:1, o:78, a:1, s:1, b:0),
% 1.09/1.48 'class_Int_Onumber' [80, 1] (w:1, o:79, a:1, s:1, b:0),
% 1.09/1.48 'c_Int_Onumber__class_Onumber__of' [82, 2] (w:1, o:157, a:1, s:1, b:0
% 1.09/1.48 ),
% 1.09/1.48 'c_HOL_Ominus__class_Ominus' [83, 3] (w:1, o:168, a:1, s:1, b:0),
% 1.09/1.48 'class_Divides_Osemiring__div' [84, 1] (w:1, o:81, a:1, s:1, b:0),
% 5.94/6.28 'class_OrderedGroup_Oab__semigroup__idem__mult' [87, 1] (w:1, o:82
% 5.94/6.28 , a:1, s:1, b:0),
% 5.94/6.28 'c_Fact_Ofact__class_Ofact' [88, 2] (w:1, o:158, a:1, s:1, b:0),
% 5.94/6.28 'class_Int_Onumber__ring' [91, 1] (w:1, o:83, a:1, s:1, b:0),
% 5.94/6.28 'class_Ring__and__Field_Odivision__ring' [92, 1] (w:1, o:85, a:1, s:1
% 5.94/6.28 , b:0),
% 5.94/6.28 'c_HOL_Oinverse__class_Oinverse' [93, 2] (w:1, o:156, a:1, s:1, b:0)
% 5.94/6.28 ,
% 5.94/6.28 'class_Ring__and__Field_Oordered__field' [94, 1] (w:1, o:86, a:1, s:1
% 5.94/6.28 , b:0),
% 5.94/6.28 'class_Ring__and__Field_Odivision__by__zero' [95, 1] (w:1, o:87, a:1
% 5.94/6.28 , s:1, b:0),
% 5.94/6.28 'c_HOL_Oinverse__class_Odivide' [97, 3] (w:1, o:169, a:1, s:1, b:0),
% 5.94/6.28
% 5.94/6.28 'class_Ring__and__Field_Osemiring__1' [98, 1] (w:1, o:92, a:1, s:1
% 5.94/6.28 , b:0),
% 5.94/6.28 'class_Ring__and__Field_Odvd' [99, 1] (w:1, o:93, a:1, s:1, b:0),
% 5.94/6.28 'class_Ring__and__Field_Ocomm__ring' [100, 1] (w:1, o:66, a:1, s:1
% 5.94/6.28 , b:0),
% 5.94/6.28 'c_Parity_Oeven__odd__class_Oeven' [103, 2] (w:1, o:159, a:1, s:1, b:
% 5.94/6.28 0),
% 5.94/6.28 'class_OrderedGroup_Oab__semigroup__mult' [104, 1] (w:1, o:94, a:1
% 5.94/6.28 , s:1, b:0),
% 5.94/6.28 'class_RealVector_Oreal__normed__algebra' [105, 1] (w:1, o:95, a:1
% 5.94/6.28 , s:1, b:0),
% 5.94/6.28 'class_Ring__and__Field_Ocomm__semiring' [110, 1] (w:1, o:84, a:1, s:
% 5.94/6.28 1, b:0),
% 5.94/6.28 'class_OrderedGroup_Ocancel__ab__semigroup__add' [111, 1] (w:1, o:96
% 5.94/6.28 , a:1, s:1, b:0),
% 5.94/6.28 'class_OrderedGroup_Ocancel__semigroup__add' [112, 1] (w:1, o:97, a:1
% 5.94/6.28 , s:1, b:0),
% 5.94/6.28 'class_Ring__and__Field_Olordered__ring' [115, 1] (w:1, o:98, a:1, s:
% 5.94/6.28 1, b:0),
% 5.94/6.28 'class_OrderedGroup_Omonoid__mult' [116, 1] (w:1, o:99, a:1, s:1, b:0
% 5.94/6.28 ),
% 5.94/6.28 'class_OrderedGroup_Ocomm__monoid__mult' [117, 1] (w:1, o:100, a:1
% 5.94/6.28 , s:1, b:0),
% 5.94/6.28 'class_Orderings_Oorder' [118, 1] (w:1, o:101, a:1, s:1, b:0),
% 5.94/6.28 'class_Orderings_Opreorder' [119, 1] (w:1, o:102, a:1, s:1, b:0),
% 5.94/6.28 'class_OrderedGroup_Ocomm__monoid__add' [120, 1] (w:1, o:103, a:1, s:
% 5.94/6.28 1, b:0),
% 5.94/6.28 'class_OrderedGroup_Oab__group__add' [121, 1] (w:1, o:104, a:1, s:1
% 5.94/6.28 , b:0),
% 5.94/6.28 'class_OrderedGroup_Oab__semigroup__add' [122, 1] (w:1, o:105, a:1
% 5.94/6.28 , s:1, b:0),
% 5.94/6.28 'class_OrderedGroup_Opordered__ab__group__add__abs' [123, 1] (w:1, o:
% 5.94/6.28 106, a:1, s:1, b:0),
% 5.94/6.28 'class_Ring__and__Field_Osemiring' [124, 1] (w:1, o:107, a:1, s:1, b:
% 5.94/6.28 0),
% 5.94/6.28 'class_Int_Oring__char__0' [125, 1] (w:1, o:108, a:1, s:1, b:0),
% 5.94/6.28 'class_OrderedGroup_Opordered__comm__monoid__add' [126, 1] (w:1, o:
% 5.94/6.28 109, a:1, s:1, b:0),
% 5.94/6.28 'class_Ring__and__Field_Oordered__comm__semiring__strict' [127, 1]
% 5.94/6.28 (w:1, o:110, a:1, s:1, b:0),
% 5.94/6.28 'class_Ring__and__Field_Opordered__ring' [130, 1] (w:1, o:112, a:1
% 5.94/6.28 , s:1, b:0),
% 5.94/6.28 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [131, 1]
% 5.94/6.28 (w:1, o:113, a:1, s:1, b:0),
% 5.94/6.28 'class_Ring__and__Field_Oring__no__zero__divisors' [133, 1] (w:1, o:
% 5.94/6.28 88, a:1, s:1, b:0),
% 5.94/6.28 'class_Ring__and__Field_Omult__zero' [134, 1] (w:1, o:114, a:1, s:1
% 5.94/6.28 , b:0),
% 5.94/6.28 'class_Ring__and__Field_Ozero__neq__one' [135, 1] (w:1, o:115, a:1
% 5.94/6.28 , s:1, b:0),
% 5.94/6.28 'class_Ring__and__Field_Ono__zero__divisors' [136, 1] (w:1, o:62, a:1
% 5.94/6.28 , s:1, b:0),
% 5.94/6.28 'class_OrderedGroup_Omonoid__add' [137, 1] (w:1, o:116, a:1, s:1, b:0
% 5.94/6.28 ),
% 5.94/6.28 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [138, 1]
% 5.94/6.28 (w:1, o:117, a:1, s:1, b:0),
% 5.94/6.28 'class_Ring__and__Field_Opordered__ring__abs' [139, 1] (w:1, o:118
% 5.94/6.28 , a:1, s:1, b:0),
% 5.94/6.28 'class_Ring__and__Field_Oordered__semiring' [140, 1] (w:1, o:111, a:1
% 5.94/6.28 , s:1, b:0),
% 5.94/6.28 'class_Ring__and__Field_Oabs__if' [141, 1] (w:1, o:119, a:1, s:1, b:0
% 5.94/6.28 ),
% 5.94/6.28 'class_Ring__and__Field_Osemiring__0' [142, 1] (w:1, o:91, a:1, s:1
% 5.94/6.28 , b:0),
% 5.94/6.28 'class_Power_Opower' [143, 1] (w:1, o:123, a:1, s:1, b:0),
% 5.94/6.28 'class_OrderedGroup_Opordered__ab__group__add' [144, 1] (w:1, o:120
% 5.94/6.28 , a:1, s:1, b:0),
% 5.94/6.28 'class_OrderedGroup_Opordered__ab__semigroup__add' [145, 1] (w:1, o:
% 5.94/6.28 121, a:1, s:1, b:0),
% 5.94/6.28 'class_Ring__and__Field_Ofield' [146, 1] (w:1, o:124, a:1, s:1, b:0)
% 5.94/6.28 ,
% 5.94/6.28 'class_Ring__and__Field_Omult__mono1' [147, 1] (w:1, o:60, a:1, s:1
% 5.94/6.28 , b:0),
% 23.37/23.72 'class_Ring__and__Field_Omult__mono' [148, 1] (w:1, o:61, a:1, s:1
% 23.37/23.72 , b:0),
% 23.37/23.72 'class_Ring__and__Field_Opordered__cancel__semiring' [149, 1] (w:1
% 23.37/23.72 , o:125, a:1, s:1, b:0),
% 23.37/23.72 'class_Ring__and__Field_Opordered__semiring' [150, 1] (w:1, o:126, a:
% 23.37/23.72 1, s:1, b:0),
% 23.37/23.72 'class_Divides_Oring__div' [153, 1] (w:1, o:80, a:1, s:1, b:0),
% 23.37/23.72 'class_Ring__and__Field_Ocomm__ring__1' [156, 1] (w:1, o:67, a:1, s:1
% 23.37/23.72 , b:0),
% 23.37/23.72 'class_OrderedGroup_Ogroup__add' [157, 1] (w:1, o:122, a:1, s:1, b:0)
% 23.37/23.72 ,
% 23.37/23.72 'class_RealVector_Oreal__field' [158, 1] (w:1, o:127, a:1, s:1, b:0)
% 23.37/23.72 ,
% 23.37/23.72 'class_RealVector_Oreal__normed__field' [160, 1] (w:1, o:128, a:1, s:
% 23.37/23.72 1, b:0),
% 23.37/23.72 'class_Ring__and__Field_Oring__1' [161, 1] (w:1, o:89, a:1, s:1, b:0)
% 23.37/23.72 ,
% 23.37/23.72 'class_Ring__and__Field_Oring__1__no__zero__divisors' [164, 1] (w:1
% 23.37/23.72 , o:90, a:1, s:1, b:0),
% 23.37/23.72 't_a' [165, 0] (w:1, o:50, a:1, s:1, b:0),
% 23.37/23.72 'v_a' [166, 0] (w:1, o:51, a:1, s:1, b:0),
% 23.37/23.72 'v_y' [167, 0] (w:1, o:52, a:1, s:1, b:0),
% 23.37/23.72 'tc_Int_Oint' [169, 0] (w:1, o:54, a:1, s:1, b:0).
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Starting Search:
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 4250
% 23.37/23.72 Kept: 2005
% 23.37/23.72 Inuse: 131
% 23.37/23.72 Deleted: 5
% 23.37/23.72 Deletedinuse: 0
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 12248
% 23.37/23.72 Kept: 4005
% 23.37/23.72 Inuse: 314
% 23.37/23.72 Deleted: 8
% 23.37/23.72 Deletedinuse: 2
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 22155
% 23.37/23.72 Kept: 6054
% 23.37/23.72 Inuse: 345
% 23.37/23.72 Deleted: 9
% 23.37/23.72 Deletedinuse: 3
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 31728
% 23.37/23.72 Kept: 8108
% 23.37/23.72 Inuse: 435
% 23.37/23.72 Deleted: 15
% 23.37/23.72 Deletedinuse: 4
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 42678
% 23.37/23.72 Kept: 10150
% 23.37/23.72 Inuse: 548
% 23.37/23.72 Deleted: 17
% 23.37/23.72 Deletedinuse: 4
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 55869
% 23.37/23.72 Kept: 12576
% 23.37/23.72 Inuse: 587
% 23.37/23.72 Deleted: 19
% 23.37/23.72 Deletedinuse: 5
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 70329
% 23.37/23.72 Kept: 14577
% 23.37/23.72 Inuse: 635
% 23.37/23.72 Deleted: 21
% 23.37/23.72 Deletedinuse: 5
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 84980
% 23.37/23.72 Kept: 17255
% 23.37/23.72 Inuse: 678
% 23.37/23.72 Deleted: 22
% 23.37/23.72 Deletedinuse: 5
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 101999
% 23.37/23.72 Kept: 19407
% 23.37/23.72 Inuse: 780
% 23.37/23.72 Deleted: 32
% 23.37/23.72 Deletedinuse: 6
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying clauses:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 116877
% 23.37/23.72 Kept: 21426
% 23.37/23.72 Inuse: 850
% 23.37/23.72 Deleted: 593
% 23.37/23.72 Deletedinuse: 7
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 133977
% 23.37/23.72 Kept: 23428
% 23.37/23.72 Inuse: 882
% 23.37/23.72 Deleted: 594
% 23.37/23.72 Deletedinuse: 8
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 146814
% 23.37/23.72 Kept: 25433
% 23.37/23.72 Inuse: 940
% 23.37/23.72 Deleted: 612
% 23.37/23.72 Deletedinuse: 24
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 158026
% 23.37/23.72 Kept: 27439
% 23.37/23.72 Inuse: 966
% 23.37/23.72 Deleted: 614
% 23.37/23.72 Deletedinuse: 24
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 171097
% 23.37/23.72 Kept: 29776
% 23.37/23.72 Inuse: 1006
% 23.37/23.72 Deleted: 614
% 23.37/23.72 Deletedinuse: 24
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 183397
% 23.37/23.72 Kept: 31862
% 23.37/23.72 Inuse: 1031
% 23.37/23.72 Deleted: 615
% 23.37/23.72 Deletedinuse: 25
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 198943
% 23.37/23.72 Kept: 34856
% 23.37/23.72 Inuse: 1066
% 23.37/23.72 Deleted: 615
% 23.37/23.72 Deletedinuse: 25
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 211234
% 23.37/23.72 Kept: 36867
% 23.37/23.72 Inuse: 1110
% 23.37/23.72 Deleted: 616
% 23.37/23.72 Deletedinuse: 26
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 220669
% 23.37/23.72 Kept: 39040
% 23.37/23.72 Inuse: 1135
% 23.37/23.72 Deleted: 617
% 23.37/23.72 Deletedinuse: 26
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 250248
% 23.37/23.72 Kept: 41987
% 23.37/23.72 Inuse: 1159
% 23.37/23.72 Deleted: 618
% 23.37/23.72 Deletedinuse: 26
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying clauses:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 276054
% 23.37/23.72 Kept: 44271
% 23.37/23.72 Inuse: 1164
% 23.37/23.72 Deleted: 1881
% 23.37/23.72 Deletedinuse: 30
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 287160
% 23.37/23.72 Kept: 47089
% 23.37/23.72 Inuse: 1174
% 23.37/23.72 Deleted: 1883
% 23.37/23.72 Deletedinuse: 32
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 304136
% 23.37/23.72 Kept: 49190
% 23.37/23.72 Inuse: 1216
% 23.37/23.72 Deleted: 1889
% 23.37/23.72 Deletedinuse: 35
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 318575
% 23.37/23.72 Kept: 51300
% 23.37/23.72 Inuse: 1260
% 23.37/23.72 Deleted: 1897
% 23.37/23.72 Deletedinuse: 42
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 342507
% 23.37/23.72 Kept: 53941
% 23.37/23.72 Inuse: 1300
% 23.37/23.72 Deleted: 1899
% 23.37/23.72 Deletedinuse: 44
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 352606
% 23.37/23.72 Kept: 55944
% 23.37/23.72 Inuse: 1328
% 23.37/23.72 Deleted: 1907
% 23.37/23.72 Deletedinuse: 52
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 371255
% 23.37/23.72 Kept: 58768
% 23.37/23.72 Inuse: 1354
% 23.37/23.72 Deleted: 1914
% 23.37/23.72 Deletedinuse: 58
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 385116
% 23.37/23.72 Kept: 60772
% 23.37/23.72 Inuse: 1378
% 23.37/23.72 Deleted: 1914
% 23.37/23.72 Deletedinuse: 58
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 393550
% 23.37/23.72 Kept: 63051
% 23.37/23.72 Inuse: 1388
% 23.37/23.72 Deleted: 1915
% 23.37/23.72 Deletedinuse: 58
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying clauses:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 415206
% 23.37/23.72 Kept: 66198
% 23.37/23.72 Inuse: 1428
% 23.37/23.72 Deleted: 3106
% 23.37/23.72 Deletedinuse: 66
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 447108
% 23.37/23.72 Kept: 70048
% 23.37/23.72 Inuse: 1437
% 23.37/23.72 Deleted: 3107
% 23.37/23.72 Deletedinuse: 66
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 460571
% 23.37/23.72 Kept: 72630
% 23.37/23.72 Inuse: 1446
% 23.37/23.72 Deleted: 3108
% 23.37/23.72 Deletedinuse: 66
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 482786
% 23.37/23.72 Kept: 74838
% 23.37/23.72 Inuse: 1506
% 23.37/23.72 Deleted: 3108
% 23.37/23.72 Deletedinuse: 66
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Intermediate Status:
% 23.37/23.72 Generated: 499445
% 23.37/23.72 Kept: 76981
% 23.37/23.72 Inuse: 1541
% 23.37/23.72 Deleted: 3108
% 23.37/23.72 Deletedinuse: 66
% 23.37/23.72
% 23.37/23.72 Resimplifying inuse:
% 23.37/23.72 Done
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 Bliksems!, er is een bewijs:
% 23.37/23.72 % SZS status Unsatisfiable
% 23.37/23.72 % SZS output start Refutation
% 23.37/23.72
% 23.37/23.72 clause( 27, [ =( 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 23.37/23.72 .
% 23.37/23.72 clause( 144, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 23.37/23.72 ] )
% 23.37/23.72 .
% 23.37/23.72 clause( 644, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), 'tc_nat' ), X ) ] )
% 23.37/23.72 .
% 23.37/23.72 clause( 792, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.72 .
% 23.37/23.72 clause( 1008, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'(
% 23.37/23.72 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 23.37/23.72 .
% 23.37/23.72 clause( 1010, [ 'c_lessequals'( 'c_Suc'( 'v_y' ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.72 .
% 23.37/23.72 clause( 1065, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 23.37/23.72 .
% 23.37/23.72 clause( 7339, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Y
% 23.37/23.72 ), X, 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.72 .
% 23.37/23.72 clause( 17688, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 23.37/23.72 .
% 23.37/23.72 clause( 17742, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 23.37/23.72 'tc_nat' ), X, 'tc_nat' ), 'c_Suc'( X ) ) ] )
% 23.37/23.72 .
% 23.37/23.72 clause( 24425, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 23.37/23.72 'c_Suc'( X ), 'tc_nat' ) ] )
% 23.37/23.72 .
% 23.37/23.72 clause( 24732, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 23.37/23.72 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 23.37/23.72 .
% 23.37/23.72 clause( 77043, [] )
% 23.37/23.72 .
% 23.37/23.72
% 23.37/23.72
% 23.37/23.72 % SZS output end Refutation
% 23.37/23.72 found a proof!
% 23.37/23.72
% 23.37/23.72 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 23.37/23.72
% 23.37/23.72 initialclauses(
% 23.37/23.72 [ clause( 77045, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 23.37/23.72 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77046, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77047, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ] )
% 23.37/23.72 , clause( 77048, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ] )
% 23.37/23.72 , clause( 77049, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 23.37/23.72 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77050, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77051, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ] )
% 23.37/23.72 , clause( 77052, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' )
% 23.37/23.72 ] )
% 23.37/23.72 , clause( 77053, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), X, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y
% 23.37/23.72 , 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77054, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77055, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77056, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 23.37/23.72 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77057, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 23.37/23.72 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77058, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77059, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77060, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 23.37/23.72 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77061, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 23.37/23.72 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77062, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 23.37/23.72 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77063, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 23.37/23.72 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77064, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 23.37/23.72 ), =( Z, Y ) ] )
% 23.37/23.72 , clause( 77065, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77066, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77067, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 23.37/23.72 , clause( 77068, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 23.37/23.72 X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77069, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 23.37/23.72 X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77070, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 23.37/23.72 ) ), =( Y, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77071, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 23.37/23.72 X, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77072, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 23.37/23.72 , clause( 77073, [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 23.37/23.72 Y, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77074, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 23.37/23.72 ) ), =( Y, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77075, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 23.37/23.72 ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y
% 23.37/23.72 , X ) ] )
% 23.37/23.72 , clause( 77076, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 23.37/23.72 , clause( 77077, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 23.37/23.72 ), =( Z, Y ) ] )
% 23.37/23.72 , clause( 77078, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 23.37/23.72 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 23.37/23.72 , Y, X ) ) ] )
% 23.37/23.72 , clause( 77079, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 23.37/23.72 X ) ), 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77080, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ),
% 23.37/23.72 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77081, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.72 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 23.37/23.72 , clause( 77082, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.72 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 23.37/23.72 , clause( 77083, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.72 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 23.37/23.72 , clause( 77084, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 23.37/23.72 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77085, [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ),
% 23.37/23.72 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77086, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 23.37/23.72 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77087, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 23.37/23.72 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 23.37/23.72 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77088, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 23.37/23.72 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 23.37/23.72 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 23.37/23.72 , clause( 77089, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77090, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77091, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 23.37/23.72 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77092, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 23.37/23.72 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77093, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 23.37/23.72 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77094, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77095, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77096, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 23.37/23.72 ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 23.37/23.72 'tc_nat' ), X ) ) ] )
% 23.37/23.72 , clause( 77097, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 23.37/23.72 , clause( 77098, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 23.37/23.72 ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77099, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77100, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.72 Z, T, X ), X ), 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 23.37/23.72 , Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77101, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 23.37/23.72 , T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77102, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 23.37/23.72 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77103, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 23.37/23.72 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 23.37/23.72 )
% 23.37/23.72 , clause( 77104, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 23.37/23.72 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 23.37/23.72 , clause( 77105, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77106, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77107, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 23.37/23.72 Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77108, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77109, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 23.37/23.72 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77110, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.72 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 23.37/23.72 , clause( 77111, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 23.37/23.72 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.72 Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 23.37/23.72 , clause( 77112, [ =( 'c_Fact_Ofact__class_Ofact'( 'c_Suc'( X ), 'tc_nat' )
% 23.37/23.72 , 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), 'c_Fact_Ofact__class_Ofact'(
% 23.37/23.72 X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77113, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 23.37/23.72 X ) ] )
% 23.37/23.72 , clause( 77114, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 23.37/23.72 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 23.37/23.72 , clause( 77115, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 23.37/23.72 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 23.37/23.72 , clause( 77116, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.72 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77117, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.72 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77118, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.72 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77119, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 23.37/23.72 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77120, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 23.37/23.72 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 23.37/23.72 , clause( 77121, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 23.37/23.72 , X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77122, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 23.37/23.72 , X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77123, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 23.37/23.72 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77124, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 23.37/23.72 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 23.37/23.72 , Y, X ) ) ] )
% 23.37/23.72 , clause( 77125, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, 'c_Divides_Odiv__class_Omod'( Y, Z,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z
% 23.37/23.72 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' )
% 23.37/23.72 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 23.37/23.72 , Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77126, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 23.37/23.72 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 23.37/23.72 ] )
% 23.37/23.72 , clause( 77127, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y, T,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77128, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77129, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 23.37/23.72 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77130, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 23.37/23.72 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77131, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77132, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 23.37/23.72 ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ] )
% 23.37/23.72 , clause( 77133, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 23.37/23.72 ), =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 23.37/23.72 , clause( 77134, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 23.37/23.72 , Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77135, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77136, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), X, 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 23.37/23.72 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77137, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 23.37/23.72 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), 'c_Power_Opower__class_Opower'( Y, X, 'tc_nat' ), 'tc_nat' )
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77138, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 23.37/23.72 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77139, [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' )
% 23.37/23.72 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Power_Opower__class_Opower'( Y
% 23.37/23.72 , 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ), 'tc_nat'
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77140, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77141, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77142, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 23.37/23.72 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ] )
% 23.37/23.72 , clause( 77143, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 23.37/23.72 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ] )
% 23.37/23.72 , clause( 77144, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Fact_Ofact__class_Ofact'( Y,
% 23.37/23.72 'tc_nat' ), X ), X ) ] )
% 23.37/23.72 , clause( 77145, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 23.37/23.72 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 23.37/23.72 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77146, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 23.37/23.72 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 23.37/23.72 T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77147, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.72 , T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.72 T, X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77148, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.72 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 Z, T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77149, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 23.37/23.72 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 23.37/23.72 , X ), T, X ) ) ] )
% 23.37/23.72 , clause( 77150, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 23.37/23.72 ), X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y
% 23.37/23.72 , T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77151, [ =( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77152, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 23.37/23.72 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 23.37/23.72 , X ), T, X ) ) ] )
% 23.37/23.72 , clause( 77153, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 23.37/23.72 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X
% 23.37/23.72 ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77154, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 23.37/23.72 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77155, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 23.37/23.72 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77156, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 23.37/23.72 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77157, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 23.37/23.72 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77158, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 23.37/23.72 ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77159, [ =( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 23.37/23.72 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77160, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 23.37/23.72 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 23.37/23.72 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77161, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 23.37/23.72 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77162, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77163, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77164, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 23.37/23.72 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 23.37/23.72 , clause( 77165, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 23.37/23.72 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77166, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), 'c_Power_Opower__class_Opower'( X, 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77167, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ] )
% 23.37/23.72 , clause( 77168, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 23.37/23.72 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 23.37/23.72 , clause( 77169, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77170, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.72 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 23.37/23.72 , clause( 77171, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77172, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77173, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77174, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77175, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77176, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77177, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77178, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77179, [ ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ) ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77180, [ ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77181, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77182, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 23.37/23.72 ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77183, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77184, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77185, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 23.37/23.72 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 23.37/23.72 X ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 23.37/23.72 , clause( 77186, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 23.37/23.72 , clause( 77187, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 23.37/23.72 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 23.37/23.72 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77188, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.72 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 23.37/23.72 , clause( 77189, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 23.37/23.72 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 23.37/23.72 , clause( 77190, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' )
% 23.37/23.72 , 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77191, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 23.37/23.72 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 23.37/23.72 , clause( 77192, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 23.37/23.72 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 23.37/23.72 , clause( 77193, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 23.37/23.72 X ), X ) ) ] )
% 23.37/23.72 , clause( 77194, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.72 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 23.37/23.72 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77195, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 23.37/23.72 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ] )
% 23.37/23.72 , clause( 77196, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ] )
% 23.37/23.72 , clause( 77197, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 23.37/23.72 , clause( 77198, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 23.37/23.72 , clause( 77199, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 23.37/23.72 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 23.37/23.72 , clause( 77200, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 23.37/23.72 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 23.37/23.72 , clause( 77201, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 23.37/23.72 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 Y, T, X ) ) ), =( Z, T ) ] )
% 23.37/23.72 , clause( 77202, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 23.37/23.72 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 T, Z, X ) ) ), =( Y, T ) ] )
% 23.37/23.72 , clause( 77203, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 23.37/23.72 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77204, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.72 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 23.37/23.72 , clause( 77205, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.72 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ] )
% 23.37/23.72 , clause( 77206, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 23.37/23.72 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77207, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77208, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 23.37/23.72 , clause( 77209, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77210, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77211, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ), 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77212, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77213, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 23.37/23.72 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77214, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 23.37/23.72 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 23.37/23.72 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 23.37/23.72 )
% 23.37/23.72 , clause( 77215, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 23.37/23.72 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 23.37/23.72 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77216, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 23.37/23.72 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 23.37/23.72 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 23.37/23.72 )
% 23.37/23.72 , clause( 77217, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77218, [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ),
% 23.37/23.72 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y
% 23.37/23.72 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y
% 23.37/23.72 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ] )
% 23.37/23.72 , clause( 77219, [ =( 'c_Fact_Ofact__class_Ofact'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ), 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77220, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 23.37/23.72 , X ) ) ] )
% 23.37/23.72 , clause( 77221, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 23.37/23.72 , clause( 77222, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 23.37/23.72 , Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ] )
% 23.37/23.72 , clause( 77223, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.72 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.72 ), X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.72 ), X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77224, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.72 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 23.37/23.72 ), X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 23.37/23.72 ), X ), X ) ) ] )
% 23.37/23.72 , clause( 77225, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77226, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 23.37/23.72 ] )
% 23.37/23.72 , clause( 77227, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 23.37/23.72 ] )
% 23.37/23.72 , clause( 77228, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 23.37/23.72 ] )
% 23.37/23.72 , clause( 77229, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77230, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77231, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77232, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 23.37/23.72 , Y, X ), X ) ] )
% 23.37/23.72 , clause( 77233, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 23.37/23.72 , Z, X ), X ) ] )
% 23.37/23.72 , clause( 77234, [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 23.37/23.72 , Z, X ), X ) ] )
% 23.37/23.72 , clause( 77235, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 23.37/23.72 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77236, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 23.37/23.72 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77237, [ =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 23.37/23.72 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77238, [ =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 23.37/23.72 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77239, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 23.37/23.72 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 23.37/23.72 ] )
% 23.37/23.72 , clause( 77240, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.72 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77241, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.72 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.72 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ] )
% 23.37/23.72 , clause( 77242, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.72 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77243, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.72 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.72 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ] )
% 23.37/23.72 , clause( 77244, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Oinverse__class_Oinverse'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 23.37/23.72 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), X ), X ), X ) ] )
% 23.37/23.72 , clause( 77245, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 Z, Y, X ) ) ] )
% 23.37/23.72 , clause( 77246, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77247, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 Z, Y, X ) ) ] )
% 23.37/23.72 , clause( 77248, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 23.37/23.72 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 23.37/23.72 , T, X ), X ), T, X ) ) ] )
% 23.37/23.72 , clause( 77249, [ ~( 'class_Orderings_Oorder'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 23.37/23.72 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 23.37/23.72 , clause( 77250, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 23.37/23.72 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77251, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.72 , 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77252, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 23.37/23.72 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77253, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 23.37/23.72 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77254, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 23.37/23.72 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 23.37/23.72 , X ) ) ] )
% 23.37/23.72 , clause( 77255, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 23.37/23.72 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77256, [ =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat'
% 23.37/23.72 ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77257, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 23.37/23.72 ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77258, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 23.37/23.72 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77259, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 23.37/23.72 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 23.37/23.72 , X ) ) ] )
% 23.37/23.72 , clause( 77260, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 23.37/23.72 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z
% 23.37/23.72 , X ) ) ] )
% 23.37/23.72 , clause( 77261, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 23.37/23.72 X ), 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X )
% 23.37/23.72 , X ) ) ] )
% 23.37/23.72 , clause( 77262, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 23.37/23.72 X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 23.37/23.72 , X ) ) ] )
% 23.37/23.72 , clause( 77263, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77264, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 23.37/23.72 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.72 Y, T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77265, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.72 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 23.37/23.72 X ) ] )
% 23.37/23.72 , clause( 77266, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), X, 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77267, [ =( 'c_Fact_Ofact__class_Ofact'(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X )
% 23.37/23.72 , Y, 'tc_nat' ), 'c_Fact_Ofact__class_Ofact'(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) )
% 23.37/23.72 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77268, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 23.37/23.72 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 23.37/23.72 , clause( 77269, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 23.37/23.72 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 23.37/23.72 , clause( 77270, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z
% 23.37/23.72 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 23.37/23.72 , T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77271, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 23.37/23.72 'tc_nat' ) ), =( Y, Z ) ] )
% 23.37/23.72 , clause( 77272, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77273, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77274, [ ~( 'class_Int_Oring__char__0'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber__ring'( X ) ), ~( =(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ] )
% 23.37/23.72 , clause( 77275, [ =( 'c_GCD_Ogcd__class_Ogcd'(
% 23.37/23.72 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat'
% 23.37/23.72 ), Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77276, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 23.37/23.72 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.72 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ] )
% 23.37/23.72 , clause( 77277, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 23.37/23.72 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 23.37/23.72 , Y, X ) ) ] )
% 23.37/23.72 , clause( 77278, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 X, Y, 'tc_nat' ), Y, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat'
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77279, [ =( 'c_GCD_Ogcd__class_Ogcd'( X,
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77280, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 23.37/23.72 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 23.37/23.72 , clause( 77281, [ =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat'
% 23.37/23.72 ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 23.37/23.72 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77282, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.72 Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77283, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.72 X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77284, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 23.37/23.72 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77285, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 23.37/23.72 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77286, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Suc'( X ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ),
% 23.37/23.72 Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77287, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 23.37/23.72 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 23.37/23.72 , 'c_Power_Opower__class_Opower'( Y, Z, X ) ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77288, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), X, 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X,
% 23.37/23.72 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77289, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.72 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77290, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 23.37/23.72 ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ] )
% 23.37/23.72 , clause( 77291, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.72 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 23.37/23.72 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 T, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ] )
% 23.37/23.72 , clause( 77292, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.72 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77293, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 23.37/23.72 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77294, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.72 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77295, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 23.37/23.72 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 23.37/23.72 , clause( 77296, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 23.37/23.72 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 23.37/23.72 , clause( 77297, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77298, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77299, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 ~( 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X
% 23.37/23.72 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77300, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77301, [ =( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 23.37/23.72 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 23.37/23.72 ] )
% 23.37/23.72 , clause( 77302, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 23.37/23.72 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 23.37/23.72 ] )
% 23.37/23.72 , clause( 77303, [ ~(
% 23.37/23.72 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 23.37/23.72 , clause( 77304, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77305, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77306, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.72 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77307, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 23.37/23.72 , clause( 77308, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77309, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 23.37/23.72 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77310, [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'(
% 23.37/23.72 X, Y, 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77311, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( X
% 23.37/23.72 , Z, 'tc_nat' ), 'c_Power_Opower__class_Opower'( Y, Z, 'tc_nat' ),
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77312, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), =( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77313, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_Power_Opower__class_Opower'( X, Z, 'tc_nat' ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), =( Z,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77314, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 23.37/23.72 ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77315, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.72 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.72 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ] )
% 23.37/23.72 , clause( 77316, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.72 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ] )
% 23.37/23.72 , clause( 77317, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.72 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ] )
% 23.37/23.72 , clause( 77318, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 23.37/23.72 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 23.37/23.72 , clause( 77319, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 23.37/23.72 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 23.37/23.72 , clause( 77320, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Power_Opower__class_Opower'( Y,
% 23.37/23.72 Z, 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77321, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.72 ), X ), X ) ) ] )
% 23.37/23.72 , clause( 77322, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 Z, Y, 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77323, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 23.37/23.72 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77324, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, X, 'tc_nat' ), X ) ] )
% 23.37/23.72 , clause( 77325, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77326, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 23.37/23.72 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ] )
% 23.37/23.72 , clause( 77327, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 23.37/23.72 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77328, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.72 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X )
% 23.37/23.72 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 23.37/23.72 , clause( 77329, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 23.37/23.72 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 23.37/23.72 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 23.37/23.72 , clause( 77330, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 23.37/23.72 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 23.37/23.72 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 23.37/23.72 , X ), W, X ) ) ] )
% 23.37/23.72 , clause( 77331, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 X ) ) ] )
% 23.37/23.72 , clause( 77332, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77333, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77334, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77335, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 23.37/23.72 , clause( 77336, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77337, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.72 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 23.37/23.72 ), X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ] )
% 23.37/23.72 , clause( 77338, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.72 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.72 ), X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ] )
% 23.37/23.72 , clause( 77339, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77340, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 23.37/23.72 Y, X ) ) ] )
% 23.37/23.72 , clause( 77341, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 X, T, 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77342, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77343, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 23.37/23.72 Y, X ) ) ] )
% 23.37/23.72 , clause( 77344, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 23.37/23.72 X ) ) ] )
% 23.37/23.72 , clause( 77345, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_Power_Opower__class_Opower'( X, Y
% 23.37/23.72 , 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77346, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 23.37/23.72 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 23.37/23.72 , T, X ), X ), T, X ) ) ] )
% 23.37/23.72 , clause( 77347, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.72 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77348, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 23.37/23.72 , T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ), T, X ) ] )
% 23.37/23.72 , clause( 77349, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 23.37/23.72 , T, X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77350, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 23.37/23.72 , T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 23.37/23.72 , T, X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77351, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 23.37/23.72 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 23.37/23.72 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 23.37/23.72 W, X ), X ) ) ] )
% 23.37/23.72 , clause( 77352, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 23.37/23.72 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 23.37/23.72 , X ), T, X ), W, X ) ) ] )
% 23.37/23.72 , clause( 77353, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 23.37/23.72 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 23.37/23.72 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 23.37/23.72 W, X ), X ) ) ] )
% 23.37/23.72 , clause( 77354, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 23.37/23.72 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 23.37/23.72 , X ), W, X ), X ) ) ] )
% 23.37/23.72 , clause( 77355, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 23.37/23.72 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 23.37/23.72 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 23.37/23.72 Z, X ) ) ] )
% 23.37/23.72 , clause( 77356, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'tc_nat' )
% 23.37/23.72 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 23.37/23.72 , 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77357, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77358, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77359, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 23.37/23.72 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77360, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 23.37/23.72 ), Z, 'tc_nat' ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 23.37/23.72 Z ), Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77361, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 23.37/23.72 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 23.37/23.72 , T ), =( X, Z ) ] )
% 23.37/23.72 , clause( 77362, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 23.37/23.72 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 23.37/23.72 , T ), =( X, Z ) ] )
% 23.37/23.72 , clause( 77363, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.72 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 23.37/23.72 =( Y, T ) ] )
% 23.37/23.72 , clause( 77364, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.72 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 23.37/23.72 =( Y, T ) ] )
% 23.37/23.72 , clause( 77365, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'tc_nat' ), =( Y
% 23.37/23.72 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77366, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'tc_nat' ), =( X
% 23.37/23.72 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77367, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 23.37/23.72 , X ) ) ] )
% 23.37/23.72 , clause( 77368, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 23.37/23.72 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77369, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 23.37/23.72 , clause( 77370, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 23.37/23.72 Y, Z, 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( Y,
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77371, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'( X
% 23.37/23.72 , Y, 'tc_nat' ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X,
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77372, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'( X
% 23.37/23.72 , Y, 'tc_nat' ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X,
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77373, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 23.37/23.72 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 23.37/23.72 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 23.37/23.72 X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77374, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), X, 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 23.37/23.72 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( X, 'c_Int_Onumber__class_Onumber__of'( Y
% 23.37/23.72 , 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77375, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77376, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), 'c_Power_Opower__class_Opower'( X,
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ), 'tc_nat' )
% 23.37/23.72 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 23.37/23.72 , 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77377, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 23.37/23.72 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.72 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77378, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 23.37/23.72 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 23.37/23.72 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77379, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_Int_Onumber__class_Onumber__of'(
% 23.37/23.72 T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 23.37/23.72 , 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.72 ), X ), X ) ) ] )
% 23.37/23.72 , clause( 77380, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77381, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77382, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77383, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 23.37/23.72 Z, X ) ) ] )
% 23.37/23.72 , clause( 77384, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 23.37/23.72 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 23.37/23.72 , clause( 77385, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 23.37/23.72 ), X ) ) ] )
% 23.37/23.72 , clause( 77386, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 23.37/23.72 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 23.37/23.72 , clause( 77387, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 23.37/23.72 , clause( 77388, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77389, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77390, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 23.37/23.72 , clause( 77391, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 23.37/23.72 , clause( 77392, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ), X ) ] )
% 23.37/23.72 , clause( 77393, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 23.37/23.72 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77394, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 23.37/23.72 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77395, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 23.37/23.72 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' )
% 23.37/23.72 , ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77396, [ ~(
% 23.37/23.72 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77397, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.72 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77398, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77399, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77400, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Oone__class_Oone'( X ), X ) ] )
% 23.37/23.72 , clause( 77401, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z
% 23.37/23.72 , 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77402, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 Z, X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 23.37/23.72 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77403, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77404, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( T, 'c_HOL_Otimes__class_Otimes'( Y, U,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ) ) ), =( 'c_Divides_Odiv__class_Omod'( X, Y,
% 23.37/23.72 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77405, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 23.37/23.72 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.72 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 23.37/23.72 , clause( 77406, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77407, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 23.37/23.72 , T ) ] )
% 23.37/23.72 , clause( 77408, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ] )
% 23.37/23.72 , clause( 77409, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77410, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.72 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 23.37/23.72 , clause( 77411, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 23.37/23.72 , clause( 77412, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77413, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.72 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 X ), T, X ) ) ] )
% 23.37/23.72 , clause( 77414, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77415, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.72 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77416, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 23.37/23.72 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77417, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 23.37/23.72 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77418, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 23.37/23.72 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77419, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 23.37/23.72 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77420, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 23.37/23.72 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77421, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 23.37/23.72 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77422, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Z, X, 'tc_nat'
% 23.37/23.72 ), 'c_Power_Opower__class_Opower'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77423, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 23.37/23.72 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Fact_Ofact__class_Ofact'( Y,
% 23.37/23.72 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 23.37/23.72 , clause( 77424, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 23.37/23.72 , clause( 77425, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77426, [ =( 'c_Divides_Odiv__class_Omod'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 23.37/23.72 ), Z, 'tc_nat' ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( Z, Y,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77427, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 23.37/23.72 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77428, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 23.37/23.72 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77429, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 23.37/23.72 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77430, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77431, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77432, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77433, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77434, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77435, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y, 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77436, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X, 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77437, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X, 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77438, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y, 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77439, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X, 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77440, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y, 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77441, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77442, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77443, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77444, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 23.37/23.72 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 23.37/23.72 , Y, X ) ) ] )
% 23.37/23.72 , clause( 77445, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77446, [ ~(
% 23.37/23.72 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 23.37/23.72 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77447, [ ~(
% 23.37/23.72 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77448, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 23.37/23.72 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77449, [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat'
% 23.37/23.72 ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77450, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.72 X ) ), ~( =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77451, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 23.37/23.72 ) ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.72 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77452, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 23.37/23.72 ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 23.37/23.72 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77453, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77454, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77455, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 23.37/23.72 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77456, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77457, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77458, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77459, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77460, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 23.37/23.72 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77461, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 23.37/23.72 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77462, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.72 , X ) ] )
% 23.37/23.72 , clause( 77463, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77464, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77465, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 23.37/23.72 =( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 23.37/23.72 )
% 23.37/23.72 , clause( 77466, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 23.37/23.72 , X ) ) ] )
% 23.37/23.72 , clause( 77467, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 23.37/23.72 =( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 23.37/23.72 )
% 23.37/23.72 , clause( 77468, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 23.37/23.72 ) ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77469, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 23.37/23.72 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77470, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 23.37/23.72 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77471, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 23.37/23.72 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77472, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 23.37/23.72 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77473, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77474, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 23.37/23.72 , =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 23.37/23.72 )
% 23.37/23.72 , clause( 77475, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.72 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 23.37/23.72 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77476, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 23.37/23.72 ] )
% 23.37/23.72 , clause( 77477, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 23.37/23.72 ] )
% 23.37/23.72 , clause( 77478, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 23.37/23.72 ] )
% 23.37/23.72 , clause( 77479, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77480, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77481, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 23.37/23.72 ] )
% 23.37/23.72 , clause( 77482, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77483, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77484, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.72 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 23.37/23.72 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 23.37/23.72 )
% 23.37/23.72 , clause( 77485, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.72 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77486, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 23.37/23.72 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77487, [ ~(
% 23.37/23.72 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 23.37/23.72 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X
% 23.37/23.72 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77488, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 23.37/23.72 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77489, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 23.37/23.72 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77490, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~(
% 23.37/23.72 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 23.37/23.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77491, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~(
% 23.37/23.72 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 23.37/23.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 23.37/23.72 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77492, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.72 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77493, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 23.37/23.72 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 23.37/23.72 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77494, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 23.37/23.72 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 23.37/23.72 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77495, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 23.37/23.72 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 23.37/23.72 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77496, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 23.37/23.72 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 23.37/23.72 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77497, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), X
% 23.37/23.72 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 23.37/23.72 , clause( 77498, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 23.37/23.72 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77499, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 23.37/23.72 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.72 , clause( 77500, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 23.37/23.72 , T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77501, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.72 , Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77502, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 23.37/23.72 , T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77503, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.72 , Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77504, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ] )
% 23.37/23.72 , clause( 77505, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.72 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77506, [ ~(
% 23.37/23.72 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 23.37/23.72 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 23.37/23.72 , clause( 77507, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 23.37/23.72 , T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77508, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.72 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.72 , Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77509, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 23.37/23.72 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ] )
% 23.37/23.72 , clause( 77510, [ ~( 'class_Int_Onumber'( X ) ), ~(
% 23.37/23.72 'class_Divides_Osemiring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 23.37/23.72 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ] )
% 23.37/23.72 , clause( 77511, [ ~( 'class_Int_Onumber'( X ) ), ~(
% 23.37/23.72 'class_Divides_Osemiring__div'( X ) ), ~( =( 'c_Divides_Odiv__class_Omod'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 23.37/23.72 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ] )
% 23.37/23.72 , clause( 77512, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.72 , 'tc_nat' ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.72 , 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77513, [ 'c_HOL_Oord__class_Oless'( 'c_Fact_Ofact__class_Ofact'(
% 23.37/23.72 X, 'tc_nat' ), 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.72 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 23.37/23.72 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77514, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.72 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'tc_nat'
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77515, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 23.37/23.72 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ] )
% 23.37/23.72 , clause( 77516, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 23.37/23.72 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 23.37/23.72 , clause( 77517, [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 23.37/23.72 , clause( 77518, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.72 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 23.37/23.72 X ), T, X ) ) ] )
% 23.37/23.72 , clause( 77519, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77520, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.72 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 23.37/23.72 X ), T, X ) ) ] )
% 23.37/23.72 , clause( 77521, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77522, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 X, Y, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77523, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77524, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 23.37/23.72 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77525, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.72 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 23.37/23.72 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 23.37/23.72 , clause( 77526, [ 'c_HOL_Oord__class_Oless'( X,
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 23.37/23.72 Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77527, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 23.37/23.72 , Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77528, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77529, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77530, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ) )
% 23.37/23.72 , 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77531, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.72 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 23.37/23.72 )
% 23.37/23.72 , clause( 77532, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 23.37/23.72 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 23.37/23.72 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77533, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77534, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 23.37/23.72 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' )
% 23.37/23.72 , ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77535, [ ~(
% 23.37/23.72 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 23.37/23.72 X ), X ) ) ] )
% 23.37/23.72 , clause( 77536, [ ~(
% 23.37/23.72 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 Z, T, X ) ) ] )
% 23.37/23.72 , clause( 77537, [ ~(
% 23.37/23.72 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 Z, T, X ) ) ] )
% 23.37/23.72 , clause( 77538, [ ~(
% 23.37/23.72 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 23.37/23.72 X ), X ) ) ] )
% 23.37/23.72 , clause( 77539, [ ~(
% 23.37/23.72 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77540, [ ~(
% 23.37/23.72 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 Y, T, X ) ) ] )
% 23.37/23.72 , clause( 77541, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.72 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.72 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 23.37/23.72 , clause( 77542, [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77543, [ =( 'c_Divides_Odiv__class_Omod'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), X, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77544, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 23.37/23.72 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77545, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 23.37/23.72 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.72 , clause( 77546, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77547, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77548, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77549, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 23.37/23.72 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77550, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.72 ) ) ] )
% 23.37/23.72 , clause( 77551, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.72 , Y, X ), X ) ) ] )
% 23.37/23.72 , clause( 77552, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 23.37/23.72 , T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77553, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 23.37/23.72 , T, X ), X ) ) ] )
% 23.37/23.72 , clause( 77554, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.72 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.72 , Y, X ), X ) ) ] )
% 23.37/23.72 , clause( 77555, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( Y, 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 23.37/23.72 ), 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77556, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 23.37/23.72 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ] )
% 23.37/23.72 , clause( 77557, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.72 , 'tc_nat' ), X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 23.37/23.72 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.72 , 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77558, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 23.37/23.72 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 23.37/23.72 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.72 , 'tc_nat' ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.72 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77559, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 23.37/23.72 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ),
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 23.37/23.72 , clause( 77560, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 23.37/23.72 X, Y, 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' )
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77561, [ =( 'c_GCD_Ogcd__class_Ogcd'( X,
% 23.37/23.72 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat'
% 23.37/23.72 ), Z, 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' )
% 23.37/23.72 ) ] )
% 23.37/23.72 , clause( 77562, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 23.37/23.72 , X ) ) ] )
% 23.37/23.72 , clause( 77563, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 23.37/23.72 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 23.37/23.72 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 23.37/23.72 , X ) ) ] )
% 23.37/23.72 , clause( 77564, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77565, [ 'c_Ring__and__Field_Odvd__class_Odvd'(
% 23.37/23.72 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77566, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 23.37/23.72 =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 23.37/23.72 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ] )
% 23.37/23.72 , clause( 77567, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.72 Y, X ) ) ] )
% 23.37/23.72 , clause( 77568, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77569, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.72 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 23.37/23.72 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.72 , clause( 77570, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.72 Y, X ) ) ] )
% 23.37/23.72 , clause( 77571, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 23.37/23.72 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.73 Y, X ) ) ] )
% 23.37/23.73 , clause( 77572, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.73 Y, X ) ) ] )
% 23.37/23.73 , clause( 77573, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 77574, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 77575, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77576, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.73 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77577, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.73 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77578, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77579, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 23.37/23.73 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77580, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 23.37/23.73 , clause( 77581, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~(
% 23.37/23.73 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77582, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77583, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.73 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 23.37/23.73 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77584, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.73 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 77585, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77586, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 23.37/23.73 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 23.37/23.73 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77587, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 23.37/23.73 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 23.37/23.73 ), X ) ] )
% 23.37/23.73 , clause( 77588, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 23.37/23.73 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 23.37/23.73 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ] )
% 23.37/23.73 , clause( 77589, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.73 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 23.37/23.73 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.73 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.73 ), X ) ] )
% 23.37/23.73 , clause( 77590, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 23.37/23.73 , clause( 77591, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77592, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 23.37/23.73 , clause( 77593, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77594, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77595, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 77596, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 23.37/23.73 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 23.37/23.73 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77597, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77598, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 23.37/23.73 , clause( 77599, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 23.37/23.73 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ] )
% 23.37/23.73 , clause( 77600, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 23.37/23.73 , clause( 77601, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 23.37/23.73 , X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 23.37/23.73 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ] )
% 23.37/23.73 , clause( 77602, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.73 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 23.37/23.73 ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.73 ), X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77603, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 23.37/23.73 ), X ) ) ] )
% 23.37/23.73 , clause( 77604, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 23.37/23.73 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 23.37/23.73 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =(
% 23.37/23.73 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 23.37/23.73 , clause( 77605, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 23.37/23.73 =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Z,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ), X ) ] )
% 23.37/23.73 , clause( 77606, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y
% 23.37/23.73 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), ~(
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77607, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 23.37/23.73 'tc_nat' ), X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 77608, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 23.37/23.73 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77609, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 23.37/23.73 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 23.37/23.73 ) ) ] )
% 23.37/23.73 , clause( 77610, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.73 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ), T, X ) ) ] )
% 23.37/23.73 , clause( 77611, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 23.37/23.73 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 23.37/23.73 ) ) ] )
% 23.37/23.73 , clause( 77612, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.73 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77613, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ), X ) ) ] )
% 23.37/23.73 , clause( 77614, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ), X ) ) ] )
% 23.37/23.73 , clause( 77615, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Fact_Ofact__class_Ofact'( Y,
% 23.37/23.73 'tc_nat' ), X ), X ) ] )
% 23.37/23.73 , clause( 77616, [ ~( 'class_Orderings_Oorder'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 23.37/23.73 , clause( 77617, [ ~( 'class_Orderings_Oorder'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 23.37/23.73 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 23.37/23.73 , clause( 77618, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 23.37/23.73 , 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 23.37/23.73 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ] )
% 23.37/23.73 , clause( 77619, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 23.37/23.73 , clause( 77620, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 23.37/23.73 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 23.37/23.73 , clause( 77621, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 23.37/23.73 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 23.37/23.73 , clause( 77622, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 23.37/23.73 , clause( 77623, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 23.37/23.73 'c_lessequals'( Y, Z, X ) ) ] )
% 23.37/23.73 , clause( 77624, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.73 X ) ), 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 23.37/23.73 , clause( 77625, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 23.37/23.73 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 23.37/23.73 ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 23.37/23.73 , clause( 77626, [ ~( 'class_Orderings_Oorder'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 23.37/23.73 , X ) ) ] )
% 23.37/23.73 , clause( 77627, [ ~( 'class_Orderings_Oorder'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 23.37/23.73 Z, Y ) ] )
% 23.37/23.73 , clause( 77628, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 23.37/23.73 , clause( 77629, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 23.37/23.73 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 23.37/23.73 , clause( 77630, [ ~( 'class_Orderings_Oorder'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 23.37/23.73 Y, Z ) ] )
% 23.37/23.73 , clause( 77631, [ ~( 'class_Orderings_Oorder'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 23.37/23.73 , X ) ) ] )
% 23.37/23.73 , clause( 77632, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 23.37/23.73 , clause( 77633, [ ~( 'class_Orderings_Oorder'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 23.37/23.73 , X ) ) ] )
% 23.37/23.73 , clause( 77634, [ ~(
% 23.37/23.73 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 77635, [ ~(
% 23.37/23.73 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 23.37/23.73 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 23.37/23.73 , clause( 77636, [ ~(
% 23.37/23.73 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 77637, [ ~(
% 23.37/23.73 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 23.37/23.73 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77638, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 23.37/23.73 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 77639, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 23.37/23.73 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 77640, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.73 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77641, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'(
% 23.37/23.73 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 23.37/23.73 , clause( 77642, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 23.37/23.73 , clause( 77643, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 23.37/23.73 Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 23.37/23.73 , clause( 77644, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 23.37/23.73 , clause( 77645, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 77646, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 23.37/23.73 , Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 23.37/23.73 , clause( 77647, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 23.37/23.73 , clause( 77648, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 23.37/23.73 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 23.37/23.73 , clause( 77649, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.73 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 23.37/23.73 , clause( 77650, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.73 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77651, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.73 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 23.37/23.73 ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ] )
% 23.37/23.73 , clause( 77652, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 23.37/23.73 , X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ] )
% 23.37/23.73 , clause( 77653, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 23.37/23.73 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ] )
% 23.37/23.73 , clause( 77654, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 23.37/23.73 , clause( 77655, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.73 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ] )
% 23.37/23.73 , clause( 77656, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.73 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'( Z,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.73 , X ), X ), X ) ) ] )
% 23.37/23.73 , clause( 77657, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ] )
% 23.37/23.73 , clause( 77658, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 Y, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), T, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 23.37/23.73 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77659, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 23.37/23.73 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77660, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.73 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.73 ), X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77661, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 23.37/23.73 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ] )
% 23.37/23.73 , clause( 77662, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 23.37/23.73 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ), T, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 23.37/23.73 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77663, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.73 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77664, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.73 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 23.37/23.73 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.73 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.73 ), X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77665, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 23.37/23.73 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 23.37/23.73 ), X ), X ) ) ] )
% 23.37/23.73 , clause( 77666, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 23.37/23.73 , clause( 77667, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 , X ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77668, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), T, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.73 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77669, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77670, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77671, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), T, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77672, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 23.37/23.73 , clause( 77673, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.73 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.73 ), X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77674, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 Y, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), T, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , X ), X ), X ) ) ] )
% 23.37/23.73 , clause( 77675, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 23.37/23.73 ), X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ] )
% 23.37/23.73 , clause( 77676, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 23.37/23.73 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.73 , X ), X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77677, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.73 Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77678, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 77679, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 77680, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Z, Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77681, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77682, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 23.37/23.73 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 77683, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 23.37/23.73 ) ) ] )
% 23.37/23.73 , clause( 77684, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 23.37/23.73 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( T, X )
% 23.37/23.73 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77685, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 23.37/23.73 , clause( 77686, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 23.37/23.73 , clause( 77687, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77688, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.73 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 77689, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 23.37/23.73 , Z, X ), Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77690, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ) ) ] )
% 23.37/23.73 , clause( 77691, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ) ) ] )
% 23.37/23.73 , clause( 77692, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 23.37/23.73 , clause( 77693, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 23.37/23.73 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 23.37/23.73 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 23.37/23.73 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77694, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 23.37/23.73 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ) ), =( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77695, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 23.37/23.73 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 23.37/23.73 Z, X ) ) ] )
% 23.37/23.73 , clause( 77696, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.73 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 , T, X ) ] )
% 23.37/23.73 , clause( 77697, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.73 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 , T, X ) ] )
% 23.37/23.73 , clause( 77698, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 23.37/23.73 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 23.37/23.73 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ),
% 23.37/23.73 ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X
% 23.37/23.73 ), X ) ) ] )
% 23.37/23.73 , clause( 77699, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 23.37/23.73 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 23.37/23.73 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 23.37/23.73 ), X ) ) ] )
% 23.37/23.73 , clause( 77700, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 23.37/23.73 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 23.37/23.73 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 , Z, X ) ] )
% 23.37/23.73 , clause( 77701, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 23.37/23.73 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 , Z, X ) ] )
% 23.37/23.73 , clause( 77702, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 23.37/23.73 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 23.37/23.73 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 23.37/23.73 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 23.37/23.73 , Y, X ) ) ] )
% 23.37/23.73 , clause( 77703, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 23.37/23.73 , clause( 77704, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 23.37/23.73 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 23.37/23.73 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 23.37/23.73 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 23.37/23.73 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77705, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 23.37/23.73 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 77706, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 23.37/23.73 ) ) ] )
% 23.37/23.73 , clause( 77707, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 23.37/23.73 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ] )
% 23.37/23.73 , clause( 77708, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ] )
% 23.37/23.73 , clause( 77709, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77710, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77711, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.73 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77712, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 23.37/23.73 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), X ), X ), X ) ] )
% 23.37/23.73 , clause( 77713, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 23.37/23.73 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77714, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.73 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 23.37/23.73 X ), T, X ) ) ] )
% 23.37/23.73 , clause( 77715, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.73 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 23.37/23.73 X ), T, X ) ) ] )
% 23.37/23.73 , clause( 77716, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T,
% 23.37/23.73 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 23.37/23.73 , Y, X ) ) ] )
% 23.37/23.73 , clause( 77717, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 23.37/23.73 , clause( 77718, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 23.37/23.73 , clause( 77719, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 23.37/23.73 ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 23.37/23.73 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 77720, [ ~(
% 23.37/23.73 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 23.37/23.73 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 23.37/23.73 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77721, [ ~(
% 23.37/23.73 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 23.37/23.73 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 23.37/23.73 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 23.37/23.73 , clause( 77722, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 23.37/23.73 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77723, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 23.37/23.73 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77724, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.73 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 77725, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.73 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77726, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77727, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77728, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77729, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 23.37/23.73 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77730, [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 77731, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 77732, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 77733, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 77734, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 77735, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77736, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77737, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77738, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ] )
% 23.37/23.73 , clause( 77739, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77740, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77741, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 23.37/23.73 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77742, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77743, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77744, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77745, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77746, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 23.37/23.73 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 23.37/23.73 , clause( 77747, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 23.37/23.73 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 23.37/23.73 , clause( 77748, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77749, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77750, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 23.37/23.73 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77751, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 23.37/23.73 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77752, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 23.37/23.73 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77753, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 23.37/23.73 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77754, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 23.37/23.73 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77755, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.73 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 77756, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 23.37/23.73 ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77757, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 23.37/23.73 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77758, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 23.37/23.73 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77759, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'(
% 23.37/23.73 X ), X ) ] )
% 23.37/23.73 , clause( 77760, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77761, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 23.37/23.73 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77762, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 23.37/23.73 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77763, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 23.37/23.73 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77764, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.73 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 23.37/23.73 , clause( 77765, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 23.37/23.73 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77766, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 23.37/23.73 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 23.37/23.73 , X ) ) ] )
% 23.37/23.73 , clause( 77767, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 23.37/23.73 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 , X ) ) ] )
% 23.37/23.73 , clause( 77768, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 23.37/23.73 ), ~( =( 'c_Power_Opower__class_Opower'( Y,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ) ) ] )
% 23.37/23.73 , clause( 77769, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77770, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77771, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 23.37/23.73 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 23.37/23.73 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 23.37/23.73 , clause( 77772, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77773, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 23.37/23.73 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 23.37/23.73 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 23.37/23.73 , clause( 77774, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.73 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77775, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.73 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77776, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77777, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77778, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77779, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77780, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 23.37/23.73 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77781, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 23.37/23.73 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77782, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 23.37/23.73 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 23.37/23.73 , clause( 77783, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 23.37/23.73 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77784, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 23.37/23.73 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 77785, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 23.37/23.73 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77786, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 23.37/23.73 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 23.37/23.73 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ] )
% 23.37/23.73 , clause( 77787, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 23.37/23.73 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77788, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.73 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77789, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.73 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77790, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ] )
% 23.37/23.73 , clause( 77791, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77792, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77793, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77794, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77795, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77796, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 23.37/23.73 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ] )
% 23.37/23.73 , clause( 77797, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 23.37/23.73 , X ) ) ] )
% 23.37/23.73 , clause( 77798, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 23.37/23.73 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 23.37/23.73 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 23.37/23.73 , clause( 77799, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 23.37/23.73 , X ) ) ] )
% 23.37/23.73 , clause( 77800, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 23.37/23.73 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 23.37/23.73 , clause( 77801, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77802, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77803, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77804, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77805, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 23.37/23.73 , clause( 77806, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 23.37/23.73 , clause( 77807, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 23.37/23.73 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ) ) ] )
% 23.37/23.73 , clause( 77808, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 23.37/23.73 , X ) ) ] )
% 23.37/23.73 , clause( 77809, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ] )
% 23.37/23.73 , clause( 77810, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77811, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 23.37/23.73 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ] )
% 23.37/23.73 , clause( 77812, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 23.37/23.73 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Z,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), T, X ) ), =( T,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77813, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 23.37/23.73 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), Z, X ) ), =( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77814, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.73 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 Y, T, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77815, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 23.37/23.73 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 Y, T, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77816, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 23.37/23.73 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 23.37/23.73 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77817, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 23.37/23.73 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77818, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 23.37/23.73 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77819, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 23.37/23.73 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 23.37/23.73 , T, X ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77820, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 23.37/23.73 X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ), T, X ) ) ] )
% 23.37/23.73 , clause( 77821, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 23.37/23.73 Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77822, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 23.37/23.73 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 23.37/23.73 X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77823, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 23.37/23.73 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 23.37/23.73 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 23.37/23.73 Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77824, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 23.37/23.73 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 23.37/23.73 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 23.37/23.73 Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77825, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 23.37/23.73 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 23.37/23.73 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 23.37/23.73 X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77826, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 23.37/23.73 ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ) ) ] )
% 23.37/23.73 , clause( 77827, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 23.37/23.73 ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ) ) ] )
% 23.37/23.73 , clause( 77828, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 23.37/23.73 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 23.37/23.73 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 23.37/23.73 ) ) ] )
% 23.37/23.73 , clause( 77829, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 23.37/23.73 ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77830, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.73 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 23.37/23.73 X ) ] )
% 23.37/23.73 , clause( 77831, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.73 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), X ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ] )
% 23.37/23.73 , clause( 77832, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 T, 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z, X ), W, X ), X ) ) ] )
% 23.37/23.73 , clause( 77833, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 23.37/23.73 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 23.37/23.73 , X ), W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X
% 23.37/23.73 ), X ) ) ] )
% 23.37/23.73 , clause( 77834, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W, X ) ) ] )
% 23.37/23.73 , clause( 77835, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ] )
% 23.37/23.73 , clause( 77836, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( T, X ), X ) )
% 23.37/23.73 , ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77837, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 23.37/23.73 'tc_nat' ), X ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77838, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , 'tc_nat' ), X ), X ) ) ] )
% 23.37/23.73 , clause( 77839, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77840, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77841, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77842, [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77843, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77844, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77845, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 77846, [ =( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77847, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77848, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 77849, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 77850, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77851, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ] )
% 23.37/23.73 , clause( 77852, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ] )
% 23.37/23.73 , clause( 77853, [ =( 'c_GCD_Ogcd__class_Ogcd'( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 23.37/23.73 , clause( 77854, [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 23.37/23.73 , clause( 77855, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77856, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77857, [ ~( =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77858, [ =( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 23.37/23.73 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77859, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 23.37/23.73 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77860, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77861, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77862, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77863, [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) )
% 23.37/23.73 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77864, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X )
% 23.37/23.73 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77865, [ =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77866, [ =( X, 'c_HOL_Oplus__class_Oplus'( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77867, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 23.37/23.73 , clause( 77868, [ =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 23.37/23.73 , clause( 77869, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 23.37/23.73 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77870, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 23.37/23.73 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 23.37/23.73 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 23.37/23.73 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 23.37/23.73 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 23.37/23.73 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 23.37/23.73 X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77871, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 23.37/23.73 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 23.37/23.73 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 23.37/23.73 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 23.37/23.73 , clause( 77872, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 23.37/23.73 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 23.37/23.73 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 23.37/23.73 , clause( 77873, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 23.37/23.73 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 23.37/23.73 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 23.37/23.73 , T, X ), X ), T, X ) ) ] )
% 23.37/23.73 , clause( 77874, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.73 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 23.37/23.73 ), X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X
% 23.37/23.73 ), X ) ) ] )
% 23.37/23.73 , clause( 77875, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 23.37/23.73 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 23.37/23.73 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 23.37/23.73 , clause( 77876, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 23.37/23.73 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 23.37/23.73 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 23.37/23.73 , clause( 77877, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 23.37/23.73 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 23.37/23.73 , clause( 77878, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 23.37/23.73 ), Y ) ] )
% 23.37/23.73 , clause( 77879, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 23.37/23.73 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 23.37/23.73 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 23.37/23.73 , clause( 77880, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 23.37/23.73 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 23.37/23.73 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 23.37/23.73 , clause( 77881, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 23.37/23.73 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 23.37/23.73 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 23.37/23.73 , clause( 77882, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 23.37/23.73 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 23.37/23.73 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 23.37/23.73 , clause( 77883, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 23.37/23.73 , U, X ), X ) ) ] )
% 23.37/23.73 , clause( 77884, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 23.37/23.73 ), Y ) ] )
% 23.37/23.73 , clause( 77885, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77886, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.73 Z, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 77887, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oinverse__class_Oinverse'(
% 23.37/23.73 Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 77888, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 23.37/23.73 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ) ) ] )
% 23.37/23.73 , clause( 77889, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 23.37/23.73 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ) ) ] )
% 23.37/23.73 , clause( 77890, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 23.37/23.73 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ) ) ] )
% 23.37/23.73 , clause( 77891, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77892, [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.73 , U, X ), X ), W, X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Z, U, X ), W, X ), X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, T, X ), W, X ), U, X ), X ) ) ] )
% 23.37/23.73 , clause( 77893, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 23.37/23.73 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ] )
% 23.37/23.73 , clause( 77894, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.73 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 23.37/23.73 Y, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77895, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 23.37/23.73 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 23.37/23.73 , clause( 77896, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 23.37/23.73 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 23.37/23.73 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 23.37/23.73 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ] )
% 23.37/23.73 , clause( 77897, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.73 =( 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 23.37/23.73 ), T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 23.37/23.73 Y, T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ] )
% 23.37/23.73 , clause( 77898, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.73 =( 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z,
% 23.37/23.73 X ), T, X ), 'c_Power_Opower__class_Opower'( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X ) ) ] )
% 23.37/23.73 , clause( 77899, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 23.37/23.73 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 23.37/23.73 ) ) ] )
% 23.37/23.73 , clause( 77900, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 23.37/23.73 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 23.37/23.73 , clause( 77901, [ 'c_HOL_Oord__class_Oless'( X,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 23.37/23.73 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77902, [ 'c_HOL_Oord__class_Oless'( X,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 23.37/23.73 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77903, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 23.37/23.73 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 23.37/23.73 ) ), Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77904, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 77905, [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77906, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77907, [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 77908, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ), 'tc_nat' ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 77909, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 23.37/23.73 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77910, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 23.37/23.73 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77911, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 23.37/23.73 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 23.37/23.73 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77912, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77913, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77914, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77915, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77916, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ] )
% 23.37/23.73 , clause( 77917, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.73 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 23.37/23.73 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ] )
% 23.37/23.73 , clause( 77918, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77919, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.73 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ] )
% 23.37/23.73 , clause( 77920, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.73 X ) ), 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 77921, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T,
% 23.37/23.73 X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 77922, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77923, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 23.37/23.73 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 77924, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 23.37/23.73 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77925, [ ~( 'class_Power_Opower'( X ) ), =(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 23.37/23.73 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 23.37/23.73 , clause( 77926, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.73 =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 23.37/23.73 , clause( 77927, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77928, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77929, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77930, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 23.37/23.73 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 , X ) ) ] )
% 23.37/23.73 , clause( 77931, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.73 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Z
% 23.37/23.73 , X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ), =( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 77932, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 23.37/23.73 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 77933, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 23.37/23.73 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 23.37/23.73 , X ) ) ] )
% 23.37/23.73 , clause( 77934, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77935, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 23.37/23.73 , clause( 77936, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 77937, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 23.37/23.73 , clause( 77938, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77939, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77940, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 77941, [ =( 'c_Fact_Ofact__class_Ofact'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77942, [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 23.37/23.73 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77943, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77944, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77945, [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 23.37/23.73 'tc_nat' ) ), Y ) ), =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77946, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 77947, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 77948, [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 23.37/23.73 ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77949, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 77950, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77951, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 77952, [ =( 'c_Power_Opower__class_Opower'( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77953, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77954, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77955, [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77956, [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 77957, [ =( 'c_Fact_Ofact__class_Ofact'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77958, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77959, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77960, [ =( 'c_Power_Opower__class_Opower'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ), 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77961, [ =( 'c_Power_Opower__class_Opower'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ), 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77962, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 23.37/23.73 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77963, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 23.37/23.73 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77964, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 23.37/23.73 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77965, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 77966, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 23.37/23.73 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77967, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 23.37/23.73 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77968, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77969, [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77970, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 23.37/23.73 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77971, [ ~( =( 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77972, [ =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 77973, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), Y, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 77974, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.73 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 77975, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.73 X ) ) ] )
% 23.37/23.73 , clause( 77976, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.73 =( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 23.37/23.73 ), X ) ) ] )
% 23.37/23.73 , clause( 77977, [ ~( 'class_Power_Opower'( X ) ), =(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 23.37/23.73 ), X ) ) ] )
% 23.37/23.73 , clause( 77978, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.73 Y, X ) ) ] )
% 23.37/23.73 , clause( 77979, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.73 =( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 23.37/23.73 ), X ) ) ] )
% 23.37/23.73 , clause( 77980, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.73 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z
% 23.37/23.73 , X ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ] )
% 23.37/23.73 , clause( 77981, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.73 =( 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 23.37/23.73 ), Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ] )
% 23.37/23.73 , clause( 77982, [ 'c_lessequals'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat'
% 23.37/23.73 ), Y, 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77983, [ 'c_lessequals'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat'
% 23.37/23.73 ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77984, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 23.37/23.73 , Z, X ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 23.37/23.73 'c_lessequals'( Z, T, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77985, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 23.37/23.73 , Z, X ), 'c_Power_Opower__class_Opower'( T, U, X ), X ), ~(
% 23.37/23.73 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 23.37/23.73 , clause( 77986, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 23.37/23.73 , Z, X ), T, X ), ~( 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 23.37/23.73 , U, X ), T, X ) ) ] )
% 23.37/23.73 , clause( 77987, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77988, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77989, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77990, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 X, Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 23.37/23.73 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77991, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X
% 23.37/23.73 ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77992, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 77993, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 23.37/23.73 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77994, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77995, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 23.37/23.73 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77996, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77997, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 23.37/23.73 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77998, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 77999, [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78000, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 23.37/23.73 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78001, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 23.37/23.73 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 23.37/23.73 , X ) ) ] )
% 23.37/23.73 , clause( 78002, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 78003, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 Y, 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 78004, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 23.37/23.73 Z, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'(
% 23.37/23.73 Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 78005, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 X, Y, 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78006, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78007, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 23.37/23.73 'tc_nat' ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78008, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X
% 23.37/23.73 , Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 78009, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ) ), 'tc_nat' ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 78010, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 78011, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 23.37/23.73 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 23.37/23.73 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 23.37/23.73 , clause( 78012, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 23.37/23.73 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 78013, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 23.37/23.73 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 Y, T, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 78014, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 23.37/23.73 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 23.37/23.73 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 23.37/23.73 , clause( 78015, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 23.37/23.73 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 23.37/23.73 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 23.37/23.73 , clause( 78016, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 78017, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 23.37/23.73 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 78018, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 23.37/23.73 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78019, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 23.37/23.73 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78020, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 23.37/23.73 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78021, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78022, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 23.37/23.73 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78023, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 23.37/23.73 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 78024, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 23.37/23.73 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 78025, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 23.37/23.73 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'(
% 23.37/23.73 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78026, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 23.37/23.73 ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78027, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X )
% 23.37/23.73 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78028, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 23.37/23.73 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78029, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat'
% 23.37/23.73 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 78030, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 23.37/23.73 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 23.37/23.73 , clause( 78031, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 23.37/23.73 ), 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78032, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78033, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78034, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78035, [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) )
% 23.37/23.73 , =( Y, Z ) ] )
% 23.37/23.73 , clause( 78036, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78037, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 23.37/23.73 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78038, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 78039, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 78040, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 23.37/23.73 ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78041, [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y,
% 23.37/23.73 'tc_nat' ), 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ),
% 23.37/23.73 =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ] )
% 23.37/23.73 , clause( 78042, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 23.37/23.73 =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 78043, [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 23.37/23.73 ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78044, [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ),
% 23.37/23.73 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78045, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 23.37/23.73 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78046, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78047, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 23.37/23.73 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78048, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 78049, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78050, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78051, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78052, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78053, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78054, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78055, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.73 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 78056, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 78057, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat'
% 23.37/23.73 ) ) ] )
% 23.37/23.73 , clause( 78058, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 23.37/23.73 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78059, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 23.37/23.73 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78060, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 23.37/23.73 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78061, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78062, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78063, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78064, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78065, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.73 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78066, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78067, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.73 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78068, [ 'c_lessequals'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat'
% 23.37/23.73 ), 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.73 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78069, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78070, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78071, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78072, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78073, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78074, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78075, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 23.37/23.73 'tc_nat' ), X, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78076, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78077, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 23.37/23.73 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78078, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 23.37/23.73 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 23.37/23.73 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 23.37/23.73 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78079, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 23.37/23.73 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 23.37/23.73 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78080, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 23.37/23.73 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 23.37/23.73 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78081, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 23.37/23.73 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78082, [ =( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 23.37/23.73 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 23.37/23.73 , 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 23.37/23.73 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 23.37/23.73 X, T, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78083, [ =( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 23.37/23.73 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 23.37/23.73 , 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 23.37/23.73 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78084, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 23.37/23.73 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z,
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 23.37/23.73 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78085, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 23.37/23.73 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ), =(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 23.37/23.73 'tc_nat' ), U ) ] )
% 23.37/23.73 , clause( 78086, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 23.37/23.73 ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78087, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 23.37/23.73 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78088, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 23.37/23.73 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78089, [ =( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 X, Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 23.37/23.73 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78090, [ =( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 Z, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z,
% 23.37/23.73 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78091, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X,
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78092, [ =( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78093, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78094, [ 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78095, [ =( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 78096, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 23.37/23.73 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 78097, [ =( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 23.37/23.73 , clause( 78098, [ =( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ) ] )
% 23.37/23.73 , clause( 78099, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 23.37/23.73 , clause( 78100, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 23.37/23.73 , clause( 78101, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 23.37/23.73 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y
% 23.37/23.73 , X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 78102, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 23.37/23.73 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 23.37/23.73 , clause( 78103, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 78104, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y
% 23.37/23.73 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 78105, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , 'tc_nat' ), X ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78106, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , 'tc_nat' ), X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), Y, X ) ), 'c_Parity_Oeven__odd__class_Oeven'(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78107, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ), 'c_Power_Opower__class_Opower'( Y,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ) ) ] )
% 23.37/23.73 , clause( 78108, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 23.37/23.73 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ), X ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Z,
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 78109, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 23.37/23.73 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 23.37/23.73 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78110, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 23.37/23.73 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 23.37/23.73 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78111, [ =( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat'
% 23.37/23.73 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78112, [ =( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78113, [ =( 'c_GCD_Ogcd__class_Ogcd'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X, 'tc_nat' ),
% 23.37/23.73 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X,
% 23.37/23.73 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78114, [ =( 'c_GCD_Ogcd__class_Ogcd'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ),
% 23.37/23.73 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X,
% 23.37/23.73 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78115, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.73 , ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Z
% 23.37/23.73 , Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78116, [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 23.37/23.73 , ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Y
% 23.37/23.73 , Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78117, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 23.37/23.73 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78118, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78119, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 23.37/23.73 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78120, [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 23.37/23.73 'tc_nat' ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 23.37/23.73 , clause( 78121, [ =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ), ~(
% 23.37/23.73 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78122, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 23.37/23.73 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78123, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 23.37/23.73 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 23.37/23.73 ), X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78124, [ =( 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 23.37/23.73 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78125, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 23.37/23.73 ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78126, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 23.37/23.73 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 23.37/23.73 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 78127, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 23.37/23.73 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 23.37/23.73 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 78128, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 23.37/23.73 ), ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 23.37/23.73 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78129, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78130, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78131, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.73 Z, T, X ), X ) ) ] )
% 23.37/23.73 , clause( 78132, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y
% 23.37/23.73 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ) ) ] )
% 23.37/23.73 , clause( 78133, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y
% 23.37/23.73 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 23.37/23.73 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 78134, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 23.37/23.73 , X ) ] )
% 23.37/23.73 , clause( 78135, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.73 ), X ) ) ] )
% 23.37/23.73 , clause( 78136, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Z, Y, X
% 23.37/23.73 ), X ) ) ] )
% 23.37/23.73 , clause( 78137, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78138, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78139, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78140, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 23.37/23.73 ), X ) ) ] )
% 23.37/23.73 , clause( 78141, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 78142, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 23.37/23.73 , clause( 78143, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 78144, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ] )
% 23.37/23.73 , clause( 78145, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 23.37/23.73 , clause( 78146, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ] )
% 23.37/23.73 , clause( 78147, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 23.37/23.73 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 78148, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 78149, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 78150, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 78151, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 78152, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 78153, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 78154, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 23.37/23.73 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 23.37/23.73 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 78155, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 78156, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 78157, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 23.37/23.73 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 23.37/23.73 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 78158, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y
% 23.37/23.73 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 78159, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 23.37/23.73 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 23.37/23.73 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 23.37/23.73 , clause( 78160, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 23.37/23.73 , X ), X ) ] )
% 23.37/23.73 , clause( 78161, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 23.37/23.73 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 23.37/23.73 X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 23.37/23.73 , clause( 78162, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 23.37/23.73 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 23.37/23.73 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78163, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 23.37/23.73 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.73 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 23.37/23.73 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78164, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 23.37/23.73 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 23.37/23.73 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 78165, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.73 X ) ) ] )
% 23.37/23.73 , clause( 78166, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 23.37/23.73 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 78167, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 78168, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 23.37/23.73 'c_lessequals'( Z, Y, X ) ) ] )
% 23.37/23.73 , clause( 78169, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 23.37/23.73 , clause( 78170, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 23.37/23.73 'c_lessequals'( Z, Y, X ) ) ] )
% 23.37/23.73 , clause( 78171, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T,
% 23.37/23.73 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78172, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 23.37/23.73 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 23.37/23.73 , Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 ) ] )
% 23.37/23.73 , clause( 78173, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ) ) ] )
% 23.37/23.73 , clause( 78174, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ) ), 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78175, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y
% 23.37/23.73 , X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78176, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 23.37/23.73 , Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78177, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ) ), 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'tc_nat'
% 23.37/23.73 ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 23.37/23.73 , X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78178, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 23.37/23.73 , ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y
% 23.37/23.73 , 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78179, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 23.37/23.73 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78180, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 X, 'c_Suc'( Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78181, [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 23.37/23.73 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 23.37/23.73 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.73 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 23.37/23.73 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 23.37/23.73 , Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78182, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( Y
% 23.37/23.73 , Z, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78183, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 23.37/23.73 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 78184, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( T, Z, X ) ) ), =( Y, T ), ~(
% 23.37/23.73 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 23.37/23.73 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 23.37/23.73 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.73 , clause( 78185, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 23.37/23.73 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 23.37/23.73 , clause( 78186, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 23.37/23.73 =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 23.37/23.73 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 78187, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 23.37/23.73 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78188, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 23.37/23.73 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z,
% 23.37/23.73 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78189, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 23.37/23.73 Z ), T, 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 23.37/23.73 'tc_nat' ), X ), Y, X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78190, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 23.37/23.73 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.73 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 78191, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 23.37/23.73 =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 78192, [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 23.37/23.73 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78193, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78194, [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78195, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 23.37/23.73 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 23.37/23.73 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.73 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.73 Z, T, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.73 , clause( 78196, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78197, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 23.37/23.73 , Y, X ) ] )
% 23.37/23.73 , clause( 78198, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y
% 23.37/23.73 , X ) ] )
% 23.37/23.73 , clause( 78199, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78200, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z,
% 23.37/23.73 Y, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78201, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78202, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 23.37/23.73 , Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 23.37/23.73 ] )
% 23.37/23.73 , clause( 78203, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 23.37/23.73 , X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 23.37/23.73 )
% 23.37/23.73 , clause( 78204, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.73 , clause( 78205, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ),
% 23.37/23.73 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78206, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 23.37/23.73 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 23.37/23.73 , clause( 78207, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 23.37/23.73 , Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 23.37/23.73 , clause( 78208, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 23.37/23.73 'tc_nat' ) ] )
% 23.37/23.73 , clause( 78209, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.73 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ), Z, X ) ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 23.37/23.73 'c_Suc'( T ), X ), 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ),
% 23.37/23.73 X ) ) ] )
% 23.37/23.73 , clause( 78210, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 23.37/23.73 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.73 X ), X ) ) ] )
% 23.37/23.73 , clause( 78211, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 23.37/23.73 ) ) ) ] )
% 23.37/23.73 , clause( 78212, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 23.37/23.73 ) ) ) ] )
% 23.37/23.73 , clause( 78213, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.73 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.73 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 23.37/23.73 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 23.37/23.73 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.74 , clause( 78214, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 23.37/23.74 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 23.37/23.74 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.74 , clause( 78215, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 23.37/23.74 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.74 , X ) ) ] )
% 23.37/23.74 , clause( 78216, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 23.37/23.74 , 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 23.37/23.74 , clause( 78217, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'(
% 23.37/23.74 Y ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78218, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 23.37/23.74 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 23.37/23.74 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 23.37/23.74 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.74 , clause( 78219, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 23.37/23.74 , clause( 78220, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 23.37/23.74 , clause( 78221, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.74 ), X ) ) ] )
% 23.37/23.74 , clause( 78222, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.74 ), X ) ) ] )
% 23.37/23.74 , clause( 78223, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.74 ), X ) ) ] )
% 23.37/23.74 , clause( 78224, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.74 ), X ) ) ] )
% 23.37/23.74 , clause( 78225, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.74 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.74 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.74 , clause( 78226, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 23.37/23.74 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.74 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.74 , clause( 78227, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 23.37/23.74 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78228, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 23.37/23.74 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78229, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 23.37/23.74 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.74 , clause( 78230, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 23.37/23.74 , X ) ) ] )
% 23.37/23.74 , clause( 78231, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 23.37/23.74 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 23.37/23.74 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.74 , clause( 78232, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78233, [ =( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( Z ),
% 23.37/23.74 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 23.37/23.74 , Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78234, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 23.37/23.74 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78235, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ),
% 23.37/23.74 ~( 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78236, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.74 ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 23.37/23.74 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 23.37/23.74 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 23.37/23.74 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.74 , clause( 78237, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.74 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 23.37/23.74 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 23.37/23.74 Y, X ), Z, X ) ) ] )
% 23.37/23.74 , clause( 78238, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78239, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 23.37/23.74 ] )
% 23.37/23.74 , clause( 78240, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 23.37/23.74 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 23.37/23.74 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 23.37/23.74 , clause( 78241, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 23.37/23.74 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 23.37/23.74 ~( 'c_lessequals'( U, T, X ) ) ] )
% 23.37/23.74 , clause( 78242, [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 23.37/23.74 =( 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 23.37/23.74 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.74 , clause( 78243, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.74 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.74 , clause( 78244, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 23.37/23.74 =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.74 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.74 ) ] )
% 23.37/23.74 , clause( 78245, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 23.37/23.74 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 23.37/23.74 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ] )
% 23.37/23.74 , clause( 78246, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 23.37/23.74 , clause( 78247, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 23.37/23.74 , clause( 78248, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.74 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 23.37/23.74 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ] )
% 23.37/23.74 , clause( 78249, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 23.37/23.74 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.74 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78250, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 23.37/23.74 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 23.37/23.74 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78251, [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 23.37/23.74 X ) ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.74 ) ) ] )
% 23.37/23.74 , clause( 78252, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 23.37/23.74 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.74 ) ) ] )
% 23.37/23.74 , clause( 78253, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 23.37/23.74 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 23.37/23.74 , clause( 78254, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 23.37/23.74 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78255, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 23.37/23.74 , clause( 78256, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 23.37/23.74 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 23.37/23.74 , clause( 78257, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 23.37/23.74 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 23.37/23.74 , clause( 78258, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.74 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 23.37/23.74 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.74 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.74 Z, T, X ), X ) ) ] )
% 23.37/23.74 , clause( 78259, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 23.37/23.74 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78260, [ ~( 'class_Ring__and__Field_Ofield'( 't_a' ) ), ~( =(
% 23.37/23.74 'v_a', 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ) ] )
% 23.37/23.74 , clause( 78261, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 23.37/23.74 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.74 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 23.37/23.74 , clause( 78262, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 23.37/23.74 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.74 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 23.37/23.74 , clause( 78263, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.74 ) ] )
% 23.37/23.74 , clause( 78264, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.74 ) ] )
% 23.37/23.74 , clause( 78265, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 23.37/23.74 ) ] )
% 23.37/23.74 , clause( 78266, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.74 ) ] )
% 23.37/23.74 , clause( 78267, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 23.37/23.74 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 23.37/23.74 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.74 , clause( 78268, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78269, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 23.37/23.74 , clause( 78270, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y,
% 23.37/23.74 'tc_nat' ), 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ),
% 23.37/23.74 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78271, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.74 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 23.37/23.74 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.74 , clause( 78272, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.74 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 23.37/23.74 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 23.37/23.74 , clause( 78273, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 23.37/23.74 ) ) ) ] )
% 23.37/23.74 , clause( 78274, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 23.37/23.74 ) ) ) ] )
% 23.37/23.74 , clause( 78275, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 23.37/23.74 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.74 , clause( 78276, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.74 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 23.37/23.74 ), X ), Y ) ] )
% 23.37/23.74 , clause( 78277, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 23.37/23.74 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.74 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 23.37/23.74 , clause( 78278, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 23.37/23.74 ), X ) ) ] )
% 23.37/23.74 , clause( 78279, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 23.37/23.74 ), X ) ) ] )
% 23.37/23.74 , clause( 78280, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 23.37/23.74 ), X ) ) ] )
% 23.37/23.74 , clause( 78281, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 23.37/23.74 ), X ) ) ] )
% 23.37/23.74 , clause( 78282, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 23.37/23.74 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 23.37/23.74 ] )
% 23.37/23.74 , clause( 78283, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 23.37/23.74 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.74 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat'
% 23.37/23.74 ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78284, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 23.37/23.74 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.74 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78285, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 23.37/23.74 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.74 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78286, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 23.37/23.74 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 23.37/23.74 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 23.37/23.74 ] )
% 23.37/23.74 , clause( 78287, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 23.37/23.74 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ] )
% 23.37/23.74 , clause( 78288, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 23.37/23.74 , T, X ) ) ), =( Z, T ) ] )
% 23.37/23.74 , clause( 78289, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 23.37/23.74 , T, X ) ) ), =( Y, Z ) ] )
% 23.37/23.74 , clause( 78290, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y
% 23.37/23.74 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 23.37/23.74 ), X ) ) ] )
% 23.37/23.74 , clause( 78291, [ =( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78292, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 23.37/23.74 'tc_nat' ), X, 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78293, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.74 ) ), =( Y, Z ) ] )
% 23.37/23.74 , clause( 78294, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.74 ) ), =( Y, Z ) ] )
% 23.37/23.74 , clause( 78295, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 23.37/23.74 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 23.37/23.74 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 23.37/23.74 , clause( 78296, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 23.37/23.74 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 23.37/23.74 'tc_nat' ), X ), 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.74 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 23.37/23.74 Y, T, X ), X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ), =( Y,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.74 , clause( 78297, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 23.37/23.74 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.74 , clause( 78298, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 23.37/23.74 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.74 , clause( 78299, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 23.37/23.74 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.74 , clause( 78300, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 23.37/23.74 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 23.37/23.74 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 23.37/23.74 , clause( 78301, [ =( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 23.37/23.74 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78302, [ =( 'c_HOL_Ominus__class_Ominus'(
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 23.37/23.74 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78303, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 23.37/23.74 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.74 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 23.37/23.74 , clause( 78304, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 23.37/23.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 23.37/23.74 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 23.37/23.74 , X ) ) ] )
% 23.37/23.74 , clause( 78305, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 23.37/23.74 X, 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78306, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 23.37/23.74 'c_lessequals'( Y, X, 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78307, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'(
% 23.37/23.74 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 23.37/23.74 , clause( 78308, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78309, [ 'class_Ring__and__Field_Ofield'( 't_a' ) ] )
% 23.37/23.74 , clause( 78310, [ 'c_lessequals'( 'c_Suc'( 'v_y' ),
% 23.37/23.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78311, [ ~( =( 'c_Power_Opower__class_Opower'(
% 23.37/23.74 'c_HOL_Oinverse__class_Oinverse'( 'v_a', 't_a' ),
% 23.37/23.74 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 23.37/23.74 'c_Suc'( 'v_y' ), 'tc_nat' ), 't_a' ), 'c_HOL_Oinverse__class_Odivide'(
% 23.37/23.74 'c_Power_Opower__class_Opower'( 'v_a', 'c_Suc'( 'v_y' ), 't_a' ),
% 23.37/23.74 'c_Power_Opower__class_Opower'( 'v_a', 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.74 'tc_nat' ), 't_a' ), 't_a' ) ) ) ] )
% 23.37/23.74 , clause( 78312, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ] )
% 23.37/23.74 , clause( 78313, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ] )
% 23.37/23.74 , clause( 78314, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ] )
% 23.37/23.74 , clause( 78315, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ] )
% 23.37/23.74 , clause( 78316, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Ono__zero__divisors'( X ) ] )
% 23.37/23.74 , clause( 78317, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ] )
% 23.37/23.74 , clause( 78318, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_OrderedGroup_Oab__semigroup__mult'( X ) ] )
% 23.37/23.74 , clause( 78319, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ] )
% 23.37/23.74 , clause( 78320, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_OrderedGroup_Oab__semigroup__add'( X ) ] )
% 23.37/23.74 , clause( 78321, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Odivision__ring'( X ) ] )
% 23.37/23.74 , clause( 78322, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Ocomm__semiring'( X ) ] )
% 23.37/23.74 , clause( 78323, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_OrderedGroup_Ocomm__monoid__add'( X ) ] )
% 23.37/23.74 , clause( 78324, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Ozero__neq__one'( X ) ] )
% 23.37/23.74 , clause( 78325, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Ocomm__ring__1'( X ) ] )
% 23.37/23.74 , clause( 78326, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Osemiring__1'( X ) ] )
% 23.37/23.74 , clause( 78327, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Osemiring__0'( X ) ] )
% 23.37/23.74 , clause( 78328, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_OrderedGroup_Oab__group__add'( X ) ] )
% 23.37/23.74 , clause( 78329, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Omult__zero'( X ) ] )
% 23.37/23.74 , clause( 78330, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Ocomm__ring'( X ) ] )
% 23.37/23.74 , clause( 78331, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_OrderedGroup_Omonoid__mult'( X ) ] )
% 23.37/23.74 , clause( 78332, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Osemiring'( X ) ] )
% 23.37/23.74 , clause( 78333, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_OrderedGroup_Omonoid__add'( X ) ] )
% 23.37/23.74 , clause( 78334, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_OrderedGroup_Ogroup__add'( X ) ] )
% 23.37/23.74 , clause( 78335, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Oring__1'( X ) ] )
% 23.37/23.74 , clause( 78336, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Oring'( X ) ] )
% 23.37/23.74 , clause( 78337, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Oidom'( X ) ] )
% 23.37/23.74 , clause( 78338, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Ring__and__Field_Odvd'( X ) ] )
% 23.37/23.74 , clause( 78339, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 23.37/23.74 'class_Power_Opower'( X ) ] )
% 23.37/23.74 , clause( 78340, [
% 23.37/23.74 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78341, [
% 23.37/23.74 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78342, [
% 23.37/23.74 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78343, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 23.37/23.74 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78344, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.74 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78345, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 23.37/23.74 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78346, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 23.37/23.74 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78347, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 23.37/23.74 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78348, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 23.37/23.74 ] )
% 23.37/23.74 , clause( 78349, [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' )
% 23.37/23.74 ] )
% 23.37/23.74 , clause( 78350, [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' )
% 23.37/23.74 ] )
% 23.37/23.74 , clause( 78351, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 23.37/23.74 ] )
% 23.37/23.74 , clause( 78352, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78353, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 23.37/23.74 ] )
% 23.37/23.74 , clause( 78354, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78355, [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78356, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78357, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78358, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78359, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78360, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78361, [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78362, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78363, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78364, [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78365, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78366, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78367, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78368, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78369, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78370, [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78371, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78372, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78373, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78374, [ 'class_Power_Opower'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78375, [ 'class_Int_Onumber'( 'tc_nat' ) ] )
% 23.37/23.74 , clause( 78376, [
% 23.37/23.74 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_Int_Oint'
% 23.37/23.74 ) ] )
% 23.37/23.74 , clause( 78377, [
% 23.37/23.74 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78378, [
% 23.37/23.74 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_Int_Oint'
% 23.37/23.74 ) ] )
% 23.37/23.74 , clause( 78379, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78380, [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78381, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78382, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78383, [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78384, [ 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78385, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78386, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78387, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78388, [ 'class_Ring__and__Field_Oordered__ring__strict'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78389, [ 'class_OrderedGroup_Opordered__ab__group__add'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78390, [ 'class_OrderedGroup_Olordered__ab__group__add'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78391, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78392, [ 'class_Ring__and__Field_Opordered__semiring'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78393, [ 'class_Ring__and__Field_Opordered__ring__abs'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78394, [ 'class_Ring__and__Field_Oordered__semiring'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78395, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78396, [ 'class_Ring__and__Field_Oordered__semidom'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78397, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 23.37/23.74 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78398, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint'
% 23.37/23.74 ) ] )
% 23.37/23.74 , clause( 78399, [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint'
% 23.37/23.74 ) ] )
% 23.37/23.74 , clause( 78400, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint'
% 23.37/23.74 ) ] )
% 23.37/23.74 , clause( 78401, [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint'
% 23.37/23.74 ) ] )
% 23.37/23.74 , clause( 78402, [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint'
% 23.37/23.74 ) ] )
% 23.37/23.74 , clause( 78403, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint'
% 23.37/23.74 ) ] )
% 23.37/23.74 , clause( 78404, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' )
% 23.37/23.74 ] )
% 23.37/23.74 , clause( 78405, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint'
% 23.37/23.74 ) ] )
% 23.37/23.74 , clause( 78406, [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' )
% 23.37/23.74 ] )
% 23.37/23.74 , clause( 78407, [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' )
% 23.37/23.74 ] )
% 23.37/23.74 , clause( 78408, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78409, [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78410, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78411, [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78412, [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78413, [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78414, [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Int_Oint' ) ]
% 23.37/23.74 )
% 23.37/23.74 , clause( 78415, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ] )
% 23.37/23.74 , clause( 78416, [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78417, [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78418, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78419, [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78420, [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78421, [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78422, [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78423, [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78424, [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78425, [ 'class_Ring__and__Field_Odvd'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78426, [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78427, [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78428, [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78429, [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78430, [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78431, [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78432, [ 'class_Power_Opower'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 , clause( 78433, [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ] )
% 23.37/23.76 ] ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 eqswap(
% 23.37/23.76 clause( 78458, [ =( 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 23.37/23.76 , clause( 77086, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 23.37/23.76 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.76 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.76 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 subsumption(
% 23.37/23.76 clause( 27, [ =( 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 23.37/23.76 , clause( 78458, [ =( 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 23.37/23.76 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 23.37/23.76 )] ) ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 subsumption(
% 23.37/23.76 clause( 144, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 23.37/23.76 ] )
% 23.37/23.76 , clause( 77226, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 23.37/23.76 ] )
% 23.37/23.76 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 23.37/23.76 ), ==>( 1, 1 )] ) ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 eqswap(
% 23.37/23.76 clause( 79338, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 23.37/23.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 23.37/23.76 , clause( 77866, [ =( X, 'c_HOL_Oplus__class_Oplus'( X,
% 23.37/23.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.76 , 0, substitution( 0, [ :=( X, X )] )).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 subsumption(
% 23.37/23.76 clause( 644, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.76 'tc_nat' ), 'tc_nat' ), X ) ] )
% 23.37/23.76 , clause( 79338, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 23.37/23.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 23.37/23.76 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 subsumption(
% 23.37/23.76 clause( 792, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 23.37/23.76 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.76 , clause( 78051, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 23.37/23.76 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.76 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 23.37/23.76 )] ) ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 subsumption(
% 23.37/23.76 clause( 1008, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'(
% 23.37/23.76 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 23.37/23.76 , clause( 78307, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'(
% 23.37/23.76 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 23.37/23.76 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 23.37/23.76 ), ==>( 1, 1 )] ) ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 subsumption(
% 23.37/23.76 clause( 1010, [ 'c_lessequals'( 'c_Suc'( 'v_y' ),
% 23.37/23.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.76 , clause( 78310, [ 'c_lessequals'( 'c_Suc'( 'v_y' ),
% 23.37/23.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.76 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 subsumption(
% 23.37/23.76 clause( 1065, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 23.37/23.76 , clause( 78365, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 23.37/23.76 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 paramod(
% 23.37/23.76 clause( 84247, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 23.37/23.76 Y ), X, 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.76 , clause( 27, [ =( 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 23.37/23.76 , 0, clause( 792, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 23.37/23.76 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.76 , 0, 2, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 23.37/23.76 :=( X, X ), :=( Y, 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) )] )
% 23.37/23.76 ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 subsumption(
% 23.37/23.76 clause( 7339, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Y
% 23.37/23.76 ), X, 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.76 , clause( 84247, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 23.37/23.76 Y ), X, 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.76 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 23.37/23.76 )] ) ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 eqswap(
% 23.37/23.76 clause( 84248, [ =( X, 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.76 'c_HOL_Oone__class_Oone'( Y ), Y ) ), ~(
% 23.37/23.76 'class_OrderedGroup_Omonoid__mult'( Y ) ) ] )
% 23.37/23.76 , clause( 144, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 23.37/23.76 ] )
% 23.37/23.76 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 resolution(
% 23.37/23.76 clause( 84249, [ =( X, 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.76 , clause( 84248, [ =( X, 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.76 'c_HOL_Oone__class_Oone'( Y ), Y ) ), ~(
% 23.37/23.76 'class_OrderedGroup_Omonoid__mult'( Y ) ) ] )
% 23.37/23.76 , 1, clause( 1065, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 23.37/23.76 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'tc_nat' )] ), substitution( 1
% 23.37/23.76 , [] )).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 eqswap(
% 23.37/23.76 clause( 84250, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 23.37/23.76 , clause( 84249, [ =( X, 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.76 , 0, substitution( 0, [ :=( X, X )] )).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 subsumption(
% 23.37/23.76 clause( 17688, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 23.37/23.76 , clause( 84250, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 23.37/23.76 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 eqswap(
% 23.37/23.76 clause( 84252, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Y ), X, 'tc_nat'
% 23.37/23.76 ), 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 23.37/23.76 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.76 , clause( 27, [ =( 'c_HOL_Oplus__class_Oplus'( Y,
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 23.37/23.76 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 paramod(
% 23.37/23.76 clause( 84255, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ),
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 23.37/23.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 23.37/23.76 'tc_nat' ) ), ~( 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ) ] )
% 23.37/23.76 , clause( 144, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 23.37/23.76 ] )
% 23.37/23.76 , 1, clause( 84252, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Y ), X,
% 23.37/23.76 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.76 Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 23.37/23.76 , 0, 10, substitution( 0, [ :=( X, 'tc_nat' ), :=( Y, X )] ),
% 23.37/23.76 substitution( 1, [ :=( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), :=( Y,
% 23.37/23.76 X )] )).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 paramod(
% 23.37/23.76 clause( 84258, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 23.37/23.76 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ), ~(
% 23.37/23.76 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ) ] )
% 23.37/23.76 , clause( 144, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 23.37/23.76 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 23.37/23.76 ] )
% 23.37/23.76 , 1, clause( 84255, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ),
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 23.37/23.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X,
% 23.37/23.76 'tc_nat' ) ), ~( 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ) ] )
% 23.37/23.76 , 0, 1, substitution( 0, [ :=( X, 'tc_nat' ), :=( Y, 'c_Suc'( X ) )] ),
% 23.37/23.76 substitution( 1, [ :=( X, X )] )).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 factor(
% 23.37/23.76 clause( 84259, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 23.37/23.76 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ) ] )
% 23.37/23.76 , clause( 84258, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 23.37/23.76 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ), ~(
% 23.37/23.76 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ) ] )
% 23.37/23.76 , 1, 2, substitution( 0, [ :=( X, X )] )).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 resolution(
% 23.37/23.76 clause( 84260, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 23.37/23.76 , clause( 84259, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 23.37/23.76 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ) ] )
% 23.37/23.76 , 1, clause( 1065, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 23.37/23.76 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 eqswap(
% 23.37/23.76 clause( 84261, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 23.37/23.76 'tc_nat' ), X, 'tc_nat' ), 'c_Suc'( X ) ) ] )
% 23.37/23.76 , clause( 84260, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 23.37/23.76 , 0, substitution( 0, [ :=( X, X )] )).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 subsumption(
% 23.37/23.76 clause( 17742, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 23.37/23.76 'tc_nat' ), X, 'tc_nat' ), 'c_Suc'( X ) ) ] )
% 23.37/23.76 , clause( 84261, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 23.37/23.76 'tc_nat' ), X, 'tc_nat' ), 'c_Suc'( X ) ) ] )
% 23.37/23.76 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 paramod(
% 23.37/23.76 clause( 84263, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 23.37/23.76 'c_Suc'( X ), 'tc_nat' ) ] )
% 23.37/23.76 , clause( 17688, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 23.37/23.76 , 0, clause( 7339, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'(
% 23.37/23.76 'c_Suc'( Y ), X, 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.76 , 0, 3, substitution( 0, [ :=( X, 'c_Suc'( X ) )] ), substitution( 1, [
% 23.37/23.76 :=( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), :=( Y, X )] )).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 subsumption(
% 23.37/23.76 clause( 24425, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 23.37/23.76 'c_Suc'( X ), 'tc_nat' ) ] )
% 23.37/23.76 , clause( 84263, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 23.37/23.76 'c_Suc'( X ), 'tc_nat' ) ] )
% 23.37/23.76 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 eqswap(
% 23.37/23.76 clause( 84264, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 23.37/23.76 , clause( 17742, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 23.37/23.76 'tc_nat' ), X, 'tc_nat' ), 'c_Suc'( X ) ) ] )
% 23.37/23.76 , 0, substitution( 0, [ :=( X, X )] )).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 paramod(
% 23.37/23.76 clause( 84266, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 23.37/23.76 , clause( 644, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 23.37/23.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 23.37/23.76 , 0, clause( 84264, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'(
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 23.37/23.76 , 0, 4, substitution( 0, [ :=( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )] )
% 23.37/23.76 , substitution( 1, [ :=( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )] )
% 23.37/23.76 ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 subsumption(
% 23.37/23.76 clause( 24732, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 23.37/23.76 , clause( 84266, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 23.37/23.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 23.37/23.76 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 23.37/23.76
% 23.37/23.76
% 23.37/23.76 resolution(
% 23.37/23.76 clause( 84269, [ ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 23.37/23.76 'tc_nat' ) ), 'c_Suc'( 'v_y' ), 'tc_nat' ) ) ] )
% 23.37/23.76 , clause( 1008, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'(
% 23.37/23.76 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 23.37/23.76 , 0, clause( 1010, [ 'c_lessequals'( 'c_Suc'( 'v_y' ),
% 23.37/23.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 23.37/23.77 , 0, substitution( 0, [ :=( X, 'c_Suc'( 'v_y' ) ), :=( Y,
% 23.37/23.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )] ), substitution( 1, [] )).
% 23.37/23.77
% 23.37/23.77
% 23.37/23.77 paramod(
% 23.37/23.77 clause( 84271, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 23.37/23.77 'c_Suc'( 'v_y' ), 'tc_nat' ) ) ] )
% 23.37/23.77 , clause( 24732, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 23.37/23.77 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 23.37/23.77 , 0, clause( 84269, [ ~( 'c_lessequals'( 'c_Suc'(
% 23.37/23.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'( 'v_y' ), 'tc_nat' ) )
% 23.37/23.77 ] )
% 23.37/23.77 , 0, 2, substitution( 0, [] ), substitution( 1, [] )).
% 23.37/23.77
% 23.37/23.77
% 23.37/23.77 resolution(
% 23.37/23.77 clause( 84272, [] )
% 23.37/23.77 , clause( 84271, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 23.37/23.77 , 'c_Suc'( 'v_y' ), 'tc_nat' ) ) ] )
% 23.37/23.77 , 0, clause( 24425, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 23.37/23.77 , 'c_Suc'( X ), 'tc_nat' ) ] )
% 23.37/23.77 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_y' )] )).
% 23.37/23.77
% 23.37/23.77
% 23.37/23.77 subsumption(
% 23.37/23.77 clause( 77043, [] )
% 23.37/23.77 , clause( 84272, [] )
% 23.37/23.77 , substitution( 0, [] ), permutation( 0, [] ) ).
% 23.37/23.77
% 23.37/23.77
% 23.37/23.77 end.
% 23.37/23.77
% 23.37/23.77 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 23.37/23.77
% 23.37/23.77 Memory use:
% 23.37/23.77
% 23.37/23.77 space for terms: 2219264
% 23.37/23.77 space for clauses: 3719241
% 23.37/23.77
% 23.37/23.77
% 23.37/23.77 clauses generated: 500327
% 23.37/23.77 clauses kept: 77044
% 23.37/23.77 clauses selected: 1544
% 23.37/23.77 clauses deleted: 3108
% 23.37/23.77 clauses inuse deleted: 66
% 23.37/23.77
% 23.37/23.77 subsentry: 2269110
% 23.37/23.77 literals s-matched: 1448983
% 23.37/23.77 literals matched: 1329624
% 23.37/23.77 full subsumption: 866285
% 23.37/23.77
% 23.37/23.77 checksum: 769601329
% 23.37/23.77
% 23.37/23.77
% 23.37/23.77 Bliksem ended
%------------------------------------------------------------------------------