TSTP Solution File: ALG396-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG396-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Thu Jul 14 12:10:43 EDT 2022
% Result : Unsatisfiable 1.01s 1.43s
% Output : Refutation 1.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG396-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : bliksem %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Tue Jun 7 22:14:19 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.01/1.42 *** allocated 10000 integers for termspace/termends
% 1.01/1.42 *** allocated 10000 integers for clauses
% 1.01/1.42 *** allocated 10000 integers for justifications
% 1.01/1.42 *** allocated 15000 integers for termspace/termends
% 1.01/1.42 *** allocated 22500 integers for termspace/termends
% 1.01/1.42 Bliksem 1.12
% 1.01/1.42
% 1.01/1.42
% 1.01/1.42 Automatic Strategy Selection
% 1.01/1.42
% 1.01/1.42 Clauses:
% 1.01/1.42 [
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.42 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.01/1.42 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.42 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.01/1.42 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.42 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.42 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.42 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.42 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.01/1.42 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.42 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.42 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.01/1.42 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.01/1.42 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.01/1.42 X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.42 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.01/1.42 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.01/1.42 Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.01/1.42 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.01/1.42 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.01/1.42 Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.42 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.01/1.42 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.01/1.42 X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.42 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.01/1.42 Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.42 X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.42 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.01/1.42 X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.42 X ), T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.42 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.42 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.42 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.01/1.42 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 1.01/1.42 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.01/1.42 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.01/1.42 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.01/1.42 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.01/1.42 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.01/1.42 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.01/1.42 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.01/1.42 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.01/1.42 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.01/1.42 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.01/1.42 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.01/1.42 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.01/1.42 ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.42 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.42 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.42 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.01/1.42 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.01/1.42 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.01/1.42 T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.01/1.42 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.01/1.42 X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.01/1.42 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.01/1.42 T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.01/1.42 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.42 X ), T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.01/1.42 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.01/1.42 T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.01/1.42 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.42 X ), T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.42 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.01/1.42 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.01/1.42 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.42 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.42 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.01/1.42 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.42 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.01/1.42 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.01/1.42 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.42 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.42 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.01/1.42 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.01/1.42 [ =( 'c_Complex_Ocnj'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.01/1.42 'tc_Complex_Ocomplex' ) ), 'c_HOL_Oplus__class_Oplus'( 'c_Complex_Ocnj'(
% 1.01/1.42 X ), 'c_Complex_Ocnj'( Y ), 'tc_Complex_Ocomplex' ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.42 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.01/1.42 , X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.01/1.42 , X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.42 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.42 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.01/1.42 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.42 , X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.42 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.42 , X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.42 , X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.42 , X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.01/1.42 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.01/1.42 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.01/1.42 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.42 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.01/1.42 X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.01/1.42 , Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.01/1.42 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 1.01/1.42 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.01/1.42 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.01/1.42 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.01/1.42 X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.01/1.42 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.01/1.42 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.01/1.42 X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.01/1.42 ), =( Z, Y ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.42 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.01/1.42 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.01/1.42 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.42 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.01/1.42 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.01/1.42 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_RealDef_Oreal' ) ), ~(
% 1.01/1.42 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ) ],
% 1.01/1.42 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.01/1.42 , X ) ) ), =( Y, Z ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.01/1.42 , X ) ) ), =( Y, Z ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.42 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.42 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.01/1.42 ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.01/1.42 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.42 ), X ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 Z, Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.01/1.42 , X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.01/1.42 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.01/1.42 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.42 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~(
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.42 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.01/1.42 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.42 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.42 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.42 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.01/1.42 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.01/1.42 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.01/1.42 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.01/1.42 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.01/1.42 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.01/1.42 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.01/1.42 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.42 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.42 , T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.42 , Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.42 , T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.42 , Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.01/1.42 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.01/1.42 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.42 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.42 Y, X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.42 , X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.01/1.42 , X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.42 , X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.01/1.42 , X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.01/1.42 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.01/1.42 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.42 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.01/1.42 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.42 X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.01/1.42 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.42 X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.01/1.42 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.42 X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.01/1.42 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.42 X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 Y, Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.42 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.01/1.42 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.01/1.42 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.42 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.01/1.42 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.01/1.42 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.01/1.42 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X
% 1.01/1.42 ), T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Oplus__class_Oplus'( Y
% 1.01/1.42 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.01/1.42 , X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.42 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.01/1.42 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.42 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.42 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.01/1.42 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.42 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.01/1.42 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.01/1.42 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.01/1.42 , X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.42 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.42 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.42 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.01/1.42 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 Y, T, X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.42 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.01/1.42 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 Y, T, X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.01/1.42 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 1.01/1.42 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.01/1.42 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.01/1.42 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.01/1.42 X ), X ), Y ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.01/1.42 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.01/1.42 X ), X ), X ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.01/1.42 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 1.01/1.42 Z, Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.42 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), Z, X ) ), =( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.42 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), T, X ) ), =( T,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 1.01/1.42 X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.42 Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.42 Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.42 Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.42 Z, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.01/1.42 , X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.01/1.42 , X ), Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.42 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.01/1.42 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.42 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.42 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.01/1.42 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X
% 1.01/1.42 ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y
% 1.01/1.42 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.01/1.42 'c_lessequals'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.01/1.42 'c_lessequals'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.01/1.42 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.01/1.42 X ) ) ), =( Z, T ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.01/1.42 X ) ) ), =( Z, T ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.01/1.42 X ) ) ), =( Y, T ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.42 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.42 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.42 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.01/1.42 , X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.01/1.42 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.01/1.42 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_OscaleR__class_OscaleR'( Y, Z
% 1.01/1.42 , X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_OscaleR__class_OscaleR'( Y, Z
% 1.01/1.42 , X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, 'c_RealVector_OscaleR__class_OscaleR'( Z
% 1.01/1.42 , T, X ), X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, 'c_RealVector_OscaleR__class_OscaleR'( Z
% 1.01/1.42 , T, X ), X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__algebra'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_OscaleR__class_OscaleR'( Y, Z
% 1.01/1.42 , X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__algebra'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, 'c_RealVector_OscaleR__class_OscaleR'( Z
% 1.01/1.42 , T, X ), X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 1.01/1.42 X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 1.01/1.42 X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.01/1.42 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.42 X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.42 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 1.01/1.42 X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.01/1.42 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.01/1.42 , T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.01/1.42 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.01/1.42 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.01/1.42 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.01/1.42 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.01/1.42 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.01/1.42 , X ), W, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.01/1.42 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.01/1.42 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.01/1.42 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.01/1.42 , X ), T, X ), W, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.42 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.01/1.42 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.42 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.01/1.42 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.01/1.42 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 1.01/1.42 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.01/1.42 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.01/1.42 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.42 Z, X ), X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.42 Z, X ), X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 1.01/1.42 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 1.01/1.42 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.01/1.42 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 1.01/1.42 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.42 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.01/1.42 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.01/1.42 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.01/1.42 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.01/1.42 , X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.01/1.42 , X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 1.01/1.42 , X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.01/1.42 ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.01/1.42 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.01/1.42 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.01/1.42 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.42 T, X ) ) ],
% 1.01/1.42 [ =( 'c_RealVector_Onorm__class_Onorm'( 'c_Complex_Ocnj'( X ),
% 1.01/1.42 'tc_Complex_Ocomplex' ), 'c_RealVector_Onorm__class_Onorm'( X,
% 1.01/1.42 'tc_Complex_Ocomplex' ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.42 , Y, X ), X ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.42 , Z, X ), X ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.42 , Z, X ), X ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.01/1.42 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.01/1.42 ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.42 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.01/1.42 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.42 Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.01/1.42 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.01/1.42 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.01/1.42 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.01/1.42 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.01/1.42 X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X
% 1.01/1.42 ), X ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.01/1.42 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.01/1.42 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.01/1.42 ],
% 1.01/1.42 [ =( 'c_Complex_Ocnj'( 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex'
% 1.01/1.42 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.01/1.42 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.42 , Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.01/1.42 ,
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.42 , Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.42 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.01/1.42 , T, X ), X ), T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.01/1.42 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.42 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.42 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.01/1.42 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.42 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.42 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.01/1.42 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.42 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.01/1.42 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.42 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.01/1.42 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.01/1.42 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.42 Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X )
% 1.01/1.42 , 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.01/1.42 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.42 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.01/1.42 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.01/1.42 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.01/1.42 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.42 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.01/1.42 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.42 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.42 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.01/1.42 ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.42 ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.01/1.42 ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.42 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.42 ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.01/1.42 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.42 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.01/1.42 X ), X ), Y ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.42 , T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.42 , Z, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 1.01/1.42 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.42 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.42 X ), T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 1.01/1.42 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.01/1.42 ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.42 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.42 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 1.01/1.42 X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( 'c_RealVector_OscaleR__class_OscaleR'( Y
% 1.01/1.42 , Z, X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.01/1.42 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.01/1.42 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.42 , U, X ), X ), W, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( Z, U, X ), W, X ), X ),
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( Y, T, X ), W, X ), U, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.01/1.42 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, U,
% 1.01/1.42 X ), X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.01/1.42 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.42 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.42 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.01/1.42 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.01/1.42 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.01/1.42 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.01/1.42 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.01/1.42 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.01/1.42 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.01/1.42 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.01/1.42 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.42 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 1.01/1.42 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.01/1.42 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.01/1.42 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.01/1.42 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.42 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.01/1.42 , X ), W, X ) ) ],
% 1.01/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.42 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.42 X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.42 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.01/1.42 , X ), 'c_RealVector_Onorm__class_Onorm'( Y, X ) ) ],
% 1.01/1.42 [ =( 'c_Complex_Ocnj'( 'c_Complex_Ocnj'( X ) ), X ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Z, T, X ), X ),
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Z, T, X ), X ),
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Z, T, X ), X ),
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.01/1.42 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.01/1.42 ) ],
% 1.01/1.42 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.42 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.43 ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.43 ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.43 ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.43 ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.01/1.43 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.01/1.43 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.01/1.43 , T, X ), X ), T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.01/1.43 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.01/1.43 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.01/1.43 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 1.01/1.43 T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.01/1.43 T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 1.01/1.43 T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.01/1.43 T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.01/1.43 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.01/1.43 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.01/1.43 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.43 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.01/1.43 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.01/1.43 , Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.01/1.43 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 , Z, X ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.01/1.43 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.01/1.43 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 , Z, X ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.01/1.43 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 1.01/1.43 ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.01/1.43 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.43 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ),
% 1.01/1.43 ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X
% 1.01/1.43 ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.01/1.43 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 , T, X ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.01/1.43 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 , T, X ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.01/1.43 Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.43 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.01/1.43 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 1.01/1.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 1.01/1.43 W, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.01/1.43 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.01/1.43 , X ), T, X ), W, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 1.01/1.43 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 1.01/1.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 1.01/1.43 W, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.01/1.43 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.01/1.43 , X ), W, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.01/1.43 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 1.01/1.43 , X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.01/1.43 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 1.01/1.43 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 1.01/1.43 Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.01/1.43 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.01/1.43 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.01/1.43 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.01/1.43 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.43 , X ), 'c_HOL_Oord__class_Oless'( Y, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 Y, 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.01/1.43 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.01/1.43 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.43 , X ), 'c_HOL_Oord__class_Oless'( T, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.01/1.43 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.43 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.01/1.43 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.43 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.01/1.43 , X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.01/1.43 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 1.01/1.43 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 1.01/1.43 X ), Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 , X ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.43 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.01/1.43 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.01/1.43 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.43 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.43 Y, Z, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.01/1.43 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.43 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( T, Y
% 1.01/1.43 , X ), Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, T
% 1.01/1.43 , X ), Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.43 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 1.01/1.43 Z, Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.01/1.43 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.01/1.43 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.01/1.43 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.01/1.43 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.01/1.43 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.43 X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.43 X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.01/1.43 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.43 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.43 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.01/1.43 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( T
% 1.01/1.43 , Z, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z
% 1.01/1.43 , T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 1.01/1.43 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.01/1.43 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.01/1.43 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.01/1.43 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.01/1.43 T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.01/1.43 T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.43 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.43 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.43 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.01/1.43 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.43 Y, T, X ), Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.01/1.43 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.43 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.43 X ), T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.43 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.01/1.43 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 1.01/1.43 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.01/1.43 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.01/1.43 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.01/1.43 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.01/1.43 ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.01/1.43 ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.01/1.43 ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.01/1.43 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.43 ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.01/1.43 ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.01/1.43 ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.01/1.43 ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.01/1.43 ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.01/1.43 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.01/1.43 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.01/1.43 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.01/1.43 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.43 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.01/1.43 , Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.01/1.43 ), Y ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.01/1.43 ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.01/1.43 ) ) ],
% 1.01/1.43 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.01/1.43 ), Y ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.01/1.43 ), Y ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.01/1.43 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.01/1.43 , X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.01/1.43 , X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.01/1.43 , X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.01/1.43 , X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.01/1.43 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.01/1.43 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.01/1.43 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.01/1.43 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 1.01/1.43 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.43 Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.43 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.01/1.43 ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.01/1.43 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.01/1.43 , Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.01/1.43 , X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.01/1.43 , Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.43 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 , X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.43 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.01/1.43 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.43 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.01/1.43 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.01/1.43 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.01/1.43 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.43 , X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 , X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.43 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.01/1.43 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( =( 'c_Complex_Ocnj'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.43 'tc_Complex_Ocomplex' ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.43 'tc_Complex_Ocomplex' ) ) ],
% 1.01/1.43 [ ~( =( 'c_Complex_Ocnj'( X ), 'c_Complex_Ocnj'( Y ) ) ), =( X, Y ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.01/1.43 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.01/1.43 X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y
% 1.01/1.43 , Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X
% 1.01/1.43 ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 1.01/1.43 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.43 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.01/1.43 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.01/1.43 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.01/1.43 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.01/1.43 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.43 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.01/1.43 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.43 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.01/1.43 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.01/1.43 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.01/1.43 X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.01/1.43 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 Z, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 Z, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.01/1.43 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.01/1.43 X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.01/1.43 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 Y, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 Y, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.01/1.43 [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Z, Y,
% 1.01/1.43 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( X, Z, 'tc_RealDef_Oreal' ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'c_lessequals'( X, X, 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.01/1.43 , X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.43 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.01/1.43 , X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 1.01/1.43 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.01/1.43 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.01/1.43 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.01/1.43 ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.01/1.43 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.01/1.43 ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.01/1.43 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.01/1.43 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.01/1.43 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 , X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__vector'( X ) ), ~( =(
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( T, Z, X ) ) ), =( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, T ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.43 ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.43 , Y, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.43 , T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.43 , T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.43 , Y, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.01/1.43 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.01/1.43 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.43 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.01/1.43 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 1.01/1.43 , X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 1.01/1.43 , X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.01/1.43 ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.01/1.43 ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.43 Y, X ), X ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.01/1.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.01/1.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.01/1.43 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.01/1.43 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.01/1.43 'c_lessequals'( Z, Y, X ) ],
% 1.01/1.43 [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), 'c_lessequals'( Y, X,
% 1.01/1.43 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.01/1.43 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.01/1.43 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.43 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.01/1.43 [ =( 'c_Polynomial_Opoly'( 'v_q____', 'c_HOL_Ominus__class_Ominus'( X,
% 1.01/1.43 'v_c____', 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 1.01/1.43 'c_Polynomial_Opoly'( 'v_pa____', X, 'tc_Complex_Ocomplex' ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.01/1.43 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.01/1.43 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.01/1.43 X ), Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ),
% 1.01/1.43 T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.01/1.43 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 1.01/1.43 'c_Polynomial_Opoly'( 'c_Polynomial_Opcompose'( Y, Z, X ), T, X ),
% 1.01/1.43 'c_Polynomial_Opoly'( Y, 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ),
% 1.01/1.43 T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.01/1.43 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.01/1.43 , T, X ), X ), T, X ) ) ],
% 1.01/1.43 [ =( 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( 'v_q____',
% 1.01/1.43 'tc_Complex_Ocomplex' ),
% 1.01/1.43 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( 'v_pa____',
% 1.01/1.43 'tc_Complex_Ocomplex' ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 1.01/1.43 ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.01/1.43 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.01/1.43 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.01/1.43 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.01/1.43 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.01/1.43 [ ~( =( 'c_Polynomial_Opoly'( 'v_pa____', 'v_c____',
% 1.01/1.43 'tc_Complex_Ocomplex' ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.43 'tc_Complex_Ocomplex' ) ) ), =( 'c_Polynomial_Opoly'( 'v_pa____',
% 1.01/1.43 'v_sko__unknown__thm__rrB__1'( 'v_pa____' ), 'tc_Complex_Ocomplex' ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ],
% 1.01/1.43 [ =( 'c_Complex_Ocnj'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.01/1.43 'tc_Complex_Ocomplex' ) ), 'c_HOL_Ominus__class_Ominus'( 'c_Complex_Ocnj'(
% 1.01/1.43 X ), 'c_Complex_Ocnj'( Y ), 'tc_Complex_Ocomplex' ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.01/1.43 , T, X ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.01/1.43 , T, X ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ],
% 1.01/1.43 [ 'c_lessequals'( 'c_RealVector_Onorm__class_Onorm'(
% 1.01/1.43 'c_Polynomial_Opoly'( 'v_pa____', 'v_c____', 'tc_Complex_Ocomplex' ),
% 1.01/1.43 'tc_Complex_Ocomplex' ), 'c_RealVector_Onorm__class_Onorm'(
% 1.01/1.43 'c_Polynomial_Opoly'( 'v_pa____', X, 'tc_Complex_Ocomplex' ),
% 1.01/1.43 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.01/1.43 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.43 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.01/1.43 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.43 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.01/1.43 [ =( 'c_Polynomial_Opoly'( 'v_q____', X, 'tc_Complex_Ocomplex' ),
% 1.01/1.43 'c_Polynomial_Opoly'( 'v_pa____', 'c_HOL_Oplus__class_Oplus'( 'v_c____',
% 1.01/1.43 X, 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.01/1.43 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.01/1.43 ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.01/1.43 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 1.01/1.43 ), Y ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.01/1.43 , T, X ) ) ), =( Z, T ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.01/1.43 , T, X ) ) ), =( Y, Z ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 ) ), =( Y, Z ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 ) ), =( Y, Z ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.01/1.43 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.01/1.43 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.43 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.01/1.43 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.43 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.01/1.43 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.01/1.43 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.01/1.43 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.01/1.43 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.01/1.43 , U, X ), X ) ) ],
% 1.01/1.43 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 1.01/1.43 'c_Polynomial_Opoly'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.01/1.43 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.43 'c_Polynomial_Opoly'( Y, T, X ), 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.43 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.01/1.43 ), X ), 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.43 Z, Y, X ), X ) ) ],
% 1.01/1.43 [ ~( =( 'c_Polynomial_Opoly'( 'v_pa____', 'v_c____',
% 1.01/1.43 'tc_Complex_Ocomplex' ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.43 'tc_Complex_Ocomplex' ) ) ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.01/1.43 ), Y ) ],
% 1.01/1.43 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.01/1.43 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ],
% 1.01/1.43 [ =( 'c_Polynomial_Opoly'( 'v_q____', 'c_HOL_Ominus__class_Ominus'( X,
% 1.01/1.43 'v_c____', 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 1.01/1.43 'c_Polynomial_Opoly'( 'v_pa____', X, 'tc_Complex_Ocomplex' ) ) ],
% 1.01/1.43 [ ~( =( 'c_Polynomial_Opoly'( 'v_pa____', 'v_x____',
% 1.01/1.43 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_q____',
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( 'v_x____', 'v_c____', 'tc_Complex_Ocomplex'
% 1.01/1.43 ), 'tc_Complex_Ocomplex' ) ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_Polynomial_Opoly'(
% 1.01/1.43 X ) ), ~( 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_Complex_Ocomplex'
% 1.01/1.43 ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_RealDef_Oreal' )
% 1.01/1.43 ],
% 1.01/1.43 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.01/1.43 ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.01/1.43 ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.01/1.43 ],
% 1.01/1.43 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.01/1.43 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.01/1.43 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.01/1.43 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.01/1.43 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.01/1.43 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_RealDef_Oreal'
% 1.01/1.43 ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 1.01/1.43 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 1.01/1.43 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_RealDef_Oreal'
% 1.01/1.43 ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_RealDef_Oreal'
% 1.01/1.43 ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_RealDef_Oreal' )
% 1.01/1.43 ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_RealDef_Oreal' )
% 1.01/1.43 ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_RealVector_Oreal__normed__vector'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__field'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_RealVector_Oreal__normed__field'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Oab__group__add'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Omult__zero'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Omult__mono'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Osemiring'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_RealVector_Oreal__algebra'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_RealVector_Oreal__vector'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oabs__if'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_RealVector_Oreal__field'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ofield'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oring'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Odvd'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.01/1.43 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.01/1.43 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.01/1.43 ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.01/1.43 ],
% 1.01/1.43 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.01/1.43 ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Complex_Ocomplex' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_RealVector_Oreal__normed__vector'( 'tc_Complex_Ocomplex' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_RealVector_Oreal__algebra'( 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_RealVector_Oreal__vector'( 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Odvd'( 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.01/1.43 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.01/1.43 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.01/1.43 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.01/1.43 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.01/1.43 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 1.01/1.43 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 1.01/1.43 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 1.01/1.43 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.43 X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.01/1.43 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 1.01/1.43 ,
% 1.01/1.43 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.01/1.43 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.43 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Polynomial_Opoly'(
% 1.01/1.43 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Polynomial_Opoly'(
% 1.01/1.43 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Polynomial_Opoly'(
% 1.01/1.43 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Polynomial_Opoly'( X
% 1.01/1.43 ) ), ~( 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Polynomial_Opoly'( X
% 1.01/1.43 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Polynomial_Opoly'(
% 1.01/1.43 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Polynomial_Opoly'( X
% 1.01/1.43 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Polynomial_Opoly'( X
% 1.01/1.43 ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Polynomial_Opoly'( X )
% 1.01/1.43 ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Polynomial_Opoly'( X
% 1.01/1.43 ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Polynomial_Opoly'( X
% 1.01/1.43 ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Polynomial_Opoly'( X )
% 1.01/1.43 ), ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Polynomial_Opoly'( X ) )
% 1.01/1.43 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Polynomial_Opoly'( X ) )
% 1.01/1.43 , ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Polynomial_Opoly'( X ) )
% 1.01/1.43 , ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Polynomial_Opoly'( X ) )
% 1.01/1.43 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Polynomial_Opoly'( X ) )
% 1.01/1.43 , ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Polynomial_Opoly'( X ) )
% 1.01/1.43 , ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Polynomial_Opoly'( X ) ),
% 1.01/1.43 ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Polynomial_Opoly'( X ) ),
% 1.01/1.43 ~( 'class_OrderedGroup_Oab__group__add'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Polynomial_Opoly'( X ) ),
% 1.01/1.43 ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Polynomial_Opoly'( X ) ),
% 1.01/1.43 ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Polynomial_Opoly'( X ) ),
% 1.01/1.43 ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Osemiring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.43 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 1.01/1.43 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.43 'class_OrderedGroup_Oab__group__add'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_Divides_Osemiring__div'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Ofield'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Ocomm__ring'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Oidom'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Oidom'( X ) ) ],
% 1.01/1.43 [ 'class_Ring__and__Field_Odvd'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 1.01/1.43 [ 'class_Orderings_Opreorder'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_Orderings_Olinorder'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_Divides_Oring__div'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Ofield'( X ) ) ],
% 1.01/1.43 [ 'class_Orderings_Oorder'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 1.01/1.43 [ 'class_Int_Onumber__ring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ]
% 1.01/1.43 ] .
% 1.01/1.43
% 1.01/1.43
% 1.01/1.43 percentage equality = 0.160505, percentage horn = 0.877060
% 1.01/1.43 This is a problem with some equality
% 1.01/1.43
% 1.01/1.43
% 1.01/1.43
% 1.01/1.43 Options Used:
% 1.01/1.43
% 1.01/1.43 useres = 1
% 1.01/1.43 useparamod = 1
% 1.01/1.43 useeqrefl = 1
% 1.01/1.43 useeqfact = 1
% 1.01/1.43 usefactor = 1
% 1.01/1.43 usesimpsplitting = 0
% 1.01/1.43 usesimpdemod = 5
% 1.01/1.43 usesimpres = 3
% 1.01/1.43
% 1.01/1.43 resimpinuse = 1000
% 1.01/1.43 resimpclauses = 20000
% 1.01/1.43 substype = eqrewr
% 1.01/1.43 backwardsubs = 1
% 1.01/1.43 selectoldest = 5
% 1.01/1.43
% 1.01/1.43 litorderings [0] = split
% 1.01/1.43 litorderings [1] = extend the termordering, first sorting on arguments
% 1.01/1.43
% 1.01/1.43 termordering = kbo
% 1.01/1.43
% 1.01/1.43 litapriori = 0
% 1.01/1.43 termapriori = 1
% 1.01/1.43 litaposteriori = 0
% 1.01/1.43 termaposteriori = 0
% 1.01/1.43 demodaposteriori = 0
% 1.01/1.43 ordereqreflfact = 0
% 1.01/1.43
% 1.01/1.43 litselect = negord
% 1.01/1.43
% 1.01/1.43 maxweight = 15
% 1.01/1.43 maxdepth = 30000
% 1.01/1.43 maxlength = 115
% 1.01/1.43 maxnrvars = 195
% 1.01/1.43 excuselevel = 1
% 1.01/1.43 increasemaxweight = 1
% 1.01/1.43
% 1.01/1.43 maxselected = 10000000
% 1.01/1.43 maxnrclauses = 10000000
% 1.01/1.43
% 1.01/1.43 showgenerated = 0
% 1.01/1.43 showkept = 0
% 1.01/1.43 showselected = 0
% 1.01/1.43 showdeleted = 0
% 1.01/1.43 showresimp = 1
% 1.01/1.43 showstatus = 2000
% 1.01/1.43
% 1.01/1.43 prologoutput = 1
% 1.01/1.43 nrgoals = 5000000
% 1.01/1.43 totalproof = 1
% 1.01/1.43
% 1.01/1.43 Symbols occurring in the translation:
% 1.01/1.43
% 1.01/1.43 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.01/1.43 . [1, 2] (w:1, o:121, a:1, s:1, b:0),
% 1.01/1.43 ! [4, 1] (w:0, o:51, a:1, s:1, b:0),
% 1.01/1.43 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.01/1.43 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Omult__mono' [40, 1] (w:1, o:57, a:1, s:1, b:
% 1.01/1.43 0),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes' [43, 3] (w:1, o:150, a:1, s:1, b:0),
% 1.01/1.43 'c_lessequals' [45, 3] (w:1, o:151, a:1, s:1, b:0),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero' [46, 1] (w:1, o:58, a:1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Opordered__ring' [47, 1] (w:1, o:68, a:1, s:1
% 1.01/1.43 , b:0),
% 1.01/1.43 'class_Ring__and__Field_Oidom' [48, 1] (w:1, o:69, a:1, s:1, b:0),
% 1.01/1.43 'class_Int_Onumber__ring' [49, 1] (w:1, o:70, a:1, s:1, b:0),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus' [52, 3] (w:1, o:153, a:1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Oordered__ring__strict' [54, 1] (w:1, o:61
% 1.01/1.43 , a:1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Oordered__field' [56, 1] (w:1, o:62, a:1, s:1
% 1.01/1.43 , b:0),
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero' [57, 1] (w:1, o:76, a:1
% 1.01/1.43 , s:1, b:0),
% 1.01/1.43 'c_HOL_Oord__class_Oless' [58, 3] (w:1, o:152, a:1, s:1, b:0),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide' [59, 3] (w:1, o:154, a:1, s:1, b:0),
% 1.01/1.43
% 1.01/1.43 'class_OrderedGroup_Oab__semigroup__idem__mult' [61, 1] (w:1, o:77
% 1.01/1.43 , a:1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Oordered__semiring__strict' [62, 1] (w:1, o:
% 1.01/1.43 63, a:1, s:1, b:0),
% 1.01/1.43 'class_Divides_Osemiring__div' [63, 1] (w:1, o:79, a:1, s:1, b:0),
% 1.01/1.43 'c_Divides_Odiv__class_Omod' [64, 3] (w:1, o:155, a:1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Odvd' [65, 1] (w:1, o:80, a:1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Ocomm__ring' [66, 1] (w:1, o:71, a:1, s:1, b:
% 1.01/1.43 0),
% 1.01/1.43 'c_HOL_Ominus__class_Ominus' [69, 3] (w:1, o:156, a:1, s:1, b:0),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd' [71, 3] (w:1, o:157, a:1, s:1
% 1.01/1.43 , b:0),
% 1.01/1.43 'class_Orderings_Olinorder' [72, 1] (w:1, o:81, a:1, s:1, b:0),
% 1.01/1.43 'c_Orderings_Oord__class_Omin' [73, 3] (w:1, o:158, a:1, s:1, b:0),
% 1.01/1.43 'c_Orderings_Oord__class_Omax' [74, 3] (w:1, o:159, a:1, s:1, b:0),
% 1.01/1.43 'class_Orderings_Oorder' [75, 1] (w:1, o:82, a:1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Opordered__cancel__semiring' [76, 1] (w:1, o:
% 1.01/1.43 83, a:1, s:1, b:0),
% 1.01/1.43 'class_OrderedGroup_Opordered__ab__group__add__abs' [77, 1] (w:1, o:
% 1.01/1.43 85, a:1, s:1, b:0),
% 1.01/1.43 'c_HOL_Oabs__class_Oabs' [78, 2] (w:1, o:146, a:1, s:1, b:0),
% 1.01/1.43 'class_OrderedGroup_Oab__semigroup__mult' [79, 1] (w:1, o:86, a:1, s:
% 1.01/1.43 1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Ocomm__semiring__1' [80, 1] (w:1, o:74, a:1
% 1.01/1.43 , s:1, b:0),
% 1.01/1.43 'class_RealVector_Oreal__normed__algebra' [85, 1] (w:1, o:87, a:1, s:
% 1.01/1.43 1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Ocomm__semiring' [90, 1] (w:1, o:75, a:1, s:1
% 1.01/1.43 , b:0),
% 1.01/1.43 'class_OrderedGroup_Olordered__ab__group__add' [92, 1] (w:1, o:88, a:
% 1.01/1.43 1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Ofield' [93, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus' [94, 2] (w:1, o:147, a:1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Omult__mono1' [95, 1] (w:1, o:90, a:1, s:1
% 1.01/1.43 , b:0),
% 1.01/1.43 'tc_Complex_Ocomplex' [96, 0] (w:1, o:34, a:1, s:1, b:0),
% 1.01/1.43 'c_Complex_Ocnj' [97, 1] (w:1, o:91, a:1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Oordered__semidom' [98, 1] (w:1, o:64, a:1
% 1.01/1.43 , s:1, b:0),
% 1.01/1.43 'class_OrderedGroup_Ogroup__add' [99, 1] (w:1, o:92, a:1, s:1, b:0),
% 1.01/1.43
% 1.01/1.43 'class_Ring__and__Field_Oordered__idom' [100, 1] (w:1, o:65, a:1, s:1
% 1.01/1.43 , b:0),
% 1.01/1.43 'class_OrderedGroup_Opordered__ab__group__add' [101, 1] (w:1, o:93
% 1.01/1.43 , a:1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Oring' [102, 1] (w:1, o:94, a:1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Opordered__ring__abs' [103, 1] (w:1, o:95, a:
% 1.01/1.43 1, s:1, b:0),
% 1.01/1.43 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [104, 1]
% 1.01/1.43 (w:1, o:96, a:1, s:1, b:0),
% 1.01/1.43 'class_OrderedGroup_Opordered__ab__semigroup__add' [105, 1] (w:1, o:
% 1.01/1.43 97, a:1, s:1, b:0),
% 1.01/1.43 'tc_RealDef_Oreal' [106, 0] (w:1, o:35, a:1, s:1, b:0),
% 1.01/1.43 'class_Lattices_Oboolean__algebra' [107, 1] (w:1, o:98, a:1, s:1, b:0
% 1.01/1.43 ),
% 1.01/1.43 'class_OrderedGroup_Olordered__ab__group__add__abs' [108, 1] (w:1, o:
% 1.01/1.43 99, a:1, s:1, b:0),
% 1.01/1.43 'class_OrderedGroup_Opordered__comm__monoid__add' [109, 1] (w:1, o:
% 1.01/1.43 100, a:1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Oring__no__zero__divisors' [110, 1] (w:1, o:
% 1.01/1.43 101, a:1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Ono__zero__divisors' [111, 1] (w:1, o:60, a:1
% 1.01/1.43 , s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Oabs__if' [112, 1] (w:1, o:102, a:1, s:1, b:0
% 1.01/1.43 ),
% 1.01/1.43 'class_Ring__and__Field_Oordered__semiring' [113, 1] (w:1, o:66, a:1
% 1.01/1.43 , s:1, b:0),
% 1.01/1.43 'class_OrderedGroup_Oordered__ab__group__add' [114, 1] (w:1, o:84, a:
% 1.01/1.43 1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Opordered__semiring' [116, 1] (w:1, o:103, a:
% 1.01/1.43 1, s:1, b:0),
% 1.01/1.43 'class_Divides_Oring__div' [117, 1] (w:1, o:78, a:1, s:1, b:0),
% 1.01/1.43 'class_OrderedGroup_Oab__group__add' [118, 1] (w:1, o:104, a:1, s:1
% 1.01/1.43 , b:0),
% 1.01/1.43 'class_Ring__and__Field_Ocomm__ring__1' [119, 1] (w:1, o:72, a:1, s:1
% 1.01/1.43 , b:0),
% 1.01/1.43 'class_OrderedGroup_Ocancel__ab__semigroup__add' [120, 1] (w:1, o:105
% 1.01/1.43 , a:1, s:1, b:0),
% 1.01/1.43 'class_OrderedGroup_Ocancel__semigroup__add' [121, 1] (w:1, o:106, a:
% 1.01/1.43 1, s:1, b:0),
% 1.01/1.43 'c_RealVector_OscaleR__class_OscaleR' [122, 3] (w:1, o:160, a:1, s:1
% 1.01/1.43 , b:0),
% 1.01/1.43 'class_RealVector_Oreal__algebra' [123, 1] (w:1, o:107, a:1, s:1, b:0
% 1.01/1.43 ),
% 1.01/1.43 'class_OrderedGroup_Ocomm__monoid__add' [127, 1] (w:1, o:108, a:1, s:
% 1.01/1.43 1, b:0),
% 1.01/1.43 'class_RealVector_Oreal__vector' [128, 1] (w:1, o:109, a:1, s:1, b:0)
% 1.01/1.43 ,
% 1.01/1.43 'class_RealVector_Oreal__normed__vector' [129, 1] (w:1, o:110, a:1
% 1.01/1.43 , s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Olordered__ring' [130, 1] (w:1, o:56, a:1, s:
% 1.01/1.43 1, b:0),
% 1.01/1.43 'c_RealVector_Onorm__class_Onorm' [131, 2] (w:1, o:148, a:1, s:1, b:0
% 1.01/1.43 ),
% 1.01/1.43 'class_Orderings_Opreorder' [132, 1] (w:1, o:111, a:1, s:1, b:0),
% 1.01/1.43 'class_OrderedGroup_Oab__semigroup__add' [133, 1] (w:1, o:112, a:1
% 1.01/1.43 , s:1, b:0),
% 1.01/1.43 'class_RealVector_Oreal__normed__field' [134, 1] (w:1, o:113, a:1, s:
% 1.01/1.43 1, b:0),
% 1.01/1.43 'class_RealVector_Oreal__field' [135, 1] (w:1, o:114, a:1, s:1, b:0)
% 1.01/1.43 ,
% 1.01/1.43 'class_Ring__and__Field_Omult__zero' [138, 1] (w:1, o:59, a:1, s:1
% 1.01/1.43 , b:0),
% 1.01/1.43 'class_Ring__and__Field_Osemiring' [139, 1] (w:1, o:115, a:1, s:1, b:
% 1.01/1.43 0),
% 1.01/1.43 'class_Ring__and__Field_Oordered__comm__semiring__strict' [140, 1]
% 1.01/1.43 (w:1, o:67, a:1, s:1, b:0),
% 1.01/1.43 'class_OrderedGroup_Omonoid__add' [141, 1] (w:1, o:116, a:1, s:1, b:0
% 1.01/1.43 ),
% 1.01/1.43 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [142, 1]
% 1.01/1.43 (w:1, o:117, a:1, s:1, b:0),
% 1.01/1.43 'v_q____' [146, 0] (w:1, o:45, a:1, s:1, b:0),
% 1.01/1.43 'v_c____' [147, 0] (w:1, o:46, a:1, s:1, b:0),
% 1.01/1.43 'c_Polynomial_Opoly' [148, 3] (w:1, o:161, a:1, s:1, b:0),
% 1.01/1.43 'v_pa____' [149, 0] (w:1, o:44, a:1, s:1, b:0),
% 1.01/1.43 'class_Ring__and__Field_Ocomm__semiring__0' [150, 1] (w:1, o:73, a:1
% 1.01/1.43 , s:1, b:0),
% 1.01/1.43 'c_Polynomial_Opcompose' [153, 3] (w:1, o:162, a:1, s:1, b:0),
% 1.01/1.43 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize' [154, 2] (w:1, o:
% 1.01/1.43 149, a:1, s:1, b:0),
% 1.01/1.43 'v_sko__unknown__thm__rrB__1' [157, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.01/1.43 'tc_Polynomial_Opoly' [158, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.01/1.43 'v_x____' [159, 0] (w:1, o:48, a:1, s:1, b:0),
% 1.01/1.43 'class_OrderedGroup_Ocancel__comm__monoid__add' [161, 1] (w:1, o:120
% 1.01/1.43 , a:1, s:1, b:0),
% 1.01/1.43 'tc_nat' [162, 0] (w:1, o:50, a:1, s:1, b:0).
% 1.01/1.43
% 1.01/1.43
% 1.01/1.43 Starting Search:
% 1.01/1.43
% 1.01/1.43
% 1.01/1.43 Bliksems!, er is een bewijs:
% 1.01/1.43 % SZS status Unsatisfiable
% 1.01/1.43 % SZS output start Refutation
% 1.01/1.43
% 1.01/1.43 clause( 563, [ =( 'c_Polynomial_Opoly'( 'v_q____',
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( X, 'v_c____', 'tc_Complex_Ocomplex' ),
% 1.01/1.43 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_pa____', X,
% 1.01/1.43 'tc_Complex_Ocomplex' ) ) ] )
% 1.01/1.43 .
% 1.01/1.43 clause( 598, [] )
% 1.01/1.43 .
% 1.01/1.43
% 1.01/1.43
% 1.01/1.43 % SZS output end Refutation
% 1.01/1.43 found a proof!
% 1.01/1.43
% 1.01/1.43 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.01/1.43
% 1.01/1.43 initialclauses(
% 1.01/1.43 [ clause( 600, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.01/1.43 ] )
% 1.01/1.43 , clause( 601, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.01/1.43 ] )
% 1.01/1.43 , clause( 602, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.01/1.43 )
% 1.01/1.43 , clause( 603, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.01/1.43 )
% 1.01/1.43 , clause( 604, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.01/1.43 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.43 , clause( 605, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X
% 1.01/1.43 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.43 ) ) ] )
% 1.01/1.43 , clause( 606, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X
% 1.01/1.43 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.43 ) ) ] )
% 1.01/1.43 , clause( 607, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.01/1.43 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.01/1.43 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.01/1.43 X ), Z, X ) ) ] )
% 1.01/1.43 , clause( 608, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.01/1.43 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.01/1.43 Z, X ), X ) ) ] )
% 1.01/1.43 , clause( 609, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.01/1.43 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.01/1.43 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.01/1.43 Z, X ), X ) ) ] )
% 1.01/1.43 , clause( 610, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.01/1.43 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.01/1.43 X ), Z, X ) ) ] )
% 1.01/1.43 , clause( 611, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.01/1.43 Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.43 X ), Z, X ) ) ] )
% 1.01/1.43 , clause( 612, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.43 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.01/1.43 X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.43 X ), T, X ) ) ] )
% 1.01/1.43 , clause( 613, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ] )
% 1.01/1.43 , clause( 614, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ] )
% 1.01/1.43 , clause( 615, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ] )
% 1.01/1.43 , clause( 616, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ] )
% 1.01/1.43 , clause( 617, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.43 , clause( 618, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 619, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 1.01/1.43 , =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 1.01/1.43 , clause( 620, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.43 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.43 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.01/1.43 , clause( 621, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.43 ) ) ] )
% 1.01/1.43 , clause( 622, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.01/1.43 ) ) ] )
% 1.01/1.43 , clause( 623, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 1.01/1.43 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ] )
% 1.01/1.43 , clause( 624, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.01/1.43 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ] )
% 1.01/1.43 , clause( 625, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.01/1.43 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.01/1.43 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 1.01/1.43 , clause( 626, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.01/1.43 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.01/1.43 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 1.01/1.43 , clause( 627, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.01/1.43 , X ) ) ] )
% 1.01/1.43 , clause( 628, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.01/1.43 , clause( 629, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.01/1.43 , X ) ) ] )
% 1.01/1.43 , clause( 630, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 1.01/1.43 Y, Z ) ] )
% 1.01/1.43 , clause( 631, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 1.01/1.43 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 1.01/1.43 , clause( 632, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.01/1.43 , clause( 633, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 1.01/1.43 Z, Y ) ] )
% 1.01/1.43 , clause( 634, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 1.01/1.43 , X ) ) ] )
% 1.01/1.43 , clause( 635, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.01/1.43 ] )
% 1.01/1.43 , clause( 636, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.01/1.43 )
% 1.01/1.43 , clause( 637, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.43 , clause( 638, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 639, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 640, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ] )
% 1.01/1.43 , clause( 641, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.43 , clause( 642, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 643, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 1.01/1.43 ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.43 , clause( 644, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.43 ) ), 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X
% 1.01/1.43 ) ] )
% 1.01/1.43 , clause( 645, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.01/1.43 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.01/1.43 T, X ), X ) ) ] )
% 1.01/1.43 , clause( 646, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.01/1.43 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.01/1.43 X ), Z, X ) ) ] )
% 1.01/1.43 , clause( 647, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.01/1.43 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.01/1.43 T, X ), X ) ) ] )
% 1.01/1.43 , clause( 648, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.01/1.43 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.43 X ), T, X ) ) ] )
% 1.01/1.43 , clause( 649, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.01/1.43 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.01/1.43 T, X ), X ) ) ] )
% 1.01/1.43 , clause( 650, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.01/1.43 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.43 X ), T, X ) ) ] )
% 1.01/1.43 , clause( 651, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.01/1.43 , clause( 652, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.01/1.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.01/1.43 , clause( 653, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.01/1.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.01/1.43 , clause( 654, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.01/1.43 , clause( 655, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.01/1.43 , clause( 656, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.01/1.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.01/1.43 , clause( 657, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.43 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.01/1.43 , clause( 658, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.01/1.43 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.01/1.43 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.43 , clause( 659, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 1.01/1.43 , clause( 660, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.43 , clause( 661, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.43 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.01/1.43 , clause( 662, [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.01/1.43 ] )
% 1.01/1.43 , clause( 663, [ =( 'c_Complex_Ocnj'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.01/1.43 'tc_Complex_Ocomplex' ) ), 'c_HOL_Oplus__class_Oplus'( 'c_Complex_Ocnj'(
% 1.01/1.43 X ), 'c_Complex_Ocnj'( Y ), 'tc_Complex_Ocomplex' ) ) ] )
% 1.01/1.43 , clause( 664, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.01/1.43 , clause( 665, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.01/1.43 , X ), Z, X ) ) ] )
% 1.01/1.43 , clause( 666, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.01/1.43 , X ), Z, X ) ) ] )
% 1.01/1.43 , clause( 667, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.43 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.01/1.43 , clause( 668, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.43 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.01/1.43 , clause( 669, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ] )
% 1.01/1.43 , clause( 670, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.43 ) ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.01/1.43 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 1.01/1.43 , clause( 671, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.43 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.43 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.01/1.43 , clause( 672, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.43 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.43 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.43 , clause( 673, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.43 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.43 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 674, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.01/1.43 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 , X ) ) ] )
% 1.01/1.43 , clause( 675, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.43 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 , X ) ) ] )
% 1.01/1.43 , clause( 676, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 , X ) ) ] )
% 1.01/1.43 , clause( 677, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 , X ) ) ] )
% 1.01/1.43 , clause( 678, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.01/1.43 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 1.01/1.43 , clause( 679, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.43 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.01/1.43 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 1.01/1.43 , clause( 680, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.01/1.43 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.01/1.43 , clause( 681, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.43 , clause( 682, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.43 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 683, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 1.01/1.43 , =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.01/1.43 , X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 1.01/1.43 , clause( 684, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.01/1.43 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 685, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.01/1.43 , clause( 686, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.01/1.43 X ), X ) ) ] )
% 1.01/1.43 , clause( 687, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.01/1.43 , Z, X ) ) ] )
% 1.01/1.43 , clause( 688, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.01/1.43 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 1.01/1.43 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 1.01/1.43 , clause( 689, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ),
% 1.01/1.43 =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X )
% 1.01/1.43 , 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 690, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ),
% 1.01/1.43 =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X )
% 1.01/1.43 , 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 691, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ),
% 1.01/1.43 =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X )
% 1.01/1.43 , 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.43 , clause( 692, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ),
% 1.01/1.43 =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X )
% 1.01/1.43 , 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.43 , clause( 693, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 1.01/1.43 , clause( 694, [ ~(
% 1.01/1.43 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.01/1.43 ) ] )
% 1.01/1.43 , clause( 695, [ ~(
% 1.01/1.43 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.01/1.43 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 1.01/1.43 , clause( 696, [ ~(
% 1.01/1.43 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.01/1.43 ) ] )
% 1.01/1.43 , clause( 697, [ ~(
% 1.01/1.43 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.01/1.43 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ) ) ] )
% 1.01/1.43 , clause( 698, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 1.01/1.43 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.01/1.43 ) ] )
% 1.01/1.43 , clause( 699, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 1.01/1.43 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.01/1.43 ) ] )
% 1.01/1.43 , clause( 700, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ] )
% 1.01/1.43 , clause( 701, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ] )
% 1.01/1.43 , clause( 702, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.01/1.43 , clause( 703, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.43 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ] )
% 1.01/1.43 , clause( 704, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.43 ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.43 , clause( 705, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ] )
% 1.01/1.43 , clause( 706, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.01/1.43 ), =( Z, Y ) ] )
% 1.01/1.43 , clause( 707, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.01/1.43 ) ] )
% 1.01/1.43 , clause( 708, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.01/1.43 ) ] )
% 1.01/1.43 , clause( 709, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 1.01/1.43 , clause( 710, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.01/1.43 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 1.01/1.43 , clause( 711, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.01/1.43 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.01/1.43 , clause( 712, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.01/1.43 ), =( Z, Y ) ] )
% 1.01/1.43 , clause( 713, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.01/1.43 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.01/1.43 , clause( 714, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_RealDef_Oreal' ) )
% 1.01/1.43 , ~( 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ) ] )
% 1.01/1.43 , clause( 715, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.01/1.43 , X ) ) ), =( Y, Z ) ] )
% 1.01/1.43 , clause( 716, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.01/1.43 , X ) ) ), =( Y, Z ) ] )
% 1.01/1.43 , clause( 717, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ] )
% 1.01/1.43 , clause( 718, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ] )
% 1.01/1.43 , clause( 719, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X
% 1.01/1.43 ) ), 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ] )
% 1.01/1.43 , clause( 720, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.43 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.43 , clause( 721, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.43 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.43 , clause( 722, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.43 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ] )
% 1.01/1.43 , clause( 723, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.43 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.01/1.43 ] )
% 1.01/1.43 , clause( 724, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 1.01/1.43 , clause( 725, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 1.01/1.43 , clause( 726, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 1.01/1.43 , clause( 727, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.01/1.43 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.43 , clause( 728, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), X
% 1.01/1.43 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 1.01/1.43 , clause( 729, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.01/1.43 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 730, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.01/1.43 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 731, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 Z, Y, X ) ) ] )
% 1.01/1.43 , clause( 732, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.01/1.43 , X ), X ) ) ] )
% 1.01/1.43 , clause( 733, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.01/1.43 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.01/1.43 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.01/1.43 ) ) ] )
% 1.01/1.43 , clause( 734, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.43 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~(
% 1.01/1.43 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ] )
% 1.01/1.43 , clause( 735, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.43 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.43 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~(
% 1.01/1.43 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 1.01/1.43 , clause( 736, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.43 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 737, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.01/1.43 ) ] )
% 1.01/1.43 , clause( 738, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.43 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 1.01/1.43 , clause( 739, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.43 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 1.01/1.43 , clause( 740, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.43 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.43 , clause( 741, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 742, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 743, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 744, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 745, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.43 , clause( 746, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 1.01/1.43 ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.43 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.43 , clause( 747, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 1.01/1.43 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.43 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.43 , clause( 748, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 1.01/1.43 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.43 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.43 , clause( 749, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.01/1.43 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.43 , clause( 750, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.01/1.43 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.43 , clause( 751, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.43 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.43 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.43 , clause( 752, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.43 ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.43 Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.43 ), X ) ) ] )
% 1.01/1.43 , clause( 753, [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.01/1.43 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.43 ) ] )
% 1.01/1.43 , clause( 754, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.01/1.43 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.01/1.43 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.01/1.43 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.43 ) ] )
% 1.01/1.43 , clause( 755, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.43 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 1.01/1.43 )
% 1.01/1.43 , clause( 756, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.43 ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.43 , T, X ), X ) ) ] )
% 1.01/1.43 , clause( 757, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.43 ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.43 , Z, X ), X ) ) ] )
% 1.01/1.43 , clause( 758, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.43 , T, X ), X ) ) ] )
% 1.01/1.43 , clause( 759, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.01/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.43 , Z, X ), X ) ) ] )
% 1.01/1.43 , clause( 760, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.43 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.01/1.43 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 1.01/1.43 , clause( 761, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.43 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.01/1.43 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ), ~(
% 1.01/1.43 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.01/1.43 , clause( 762, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.43 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.43 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.43 Y, X ), Z, X ) ) ] )
% 1.01/1.43 , clause( 763, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.43 , X ) ) ] )
% 1.01/1.43 , clause( 764, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.01/1.43 , X ) ) ] )
% 1.01/1.43 , clause( 765, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.43 , X ) ) ] )
% 1.01/1.43 , clause( 766, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.01/1.43 , X ) ) ] )
% 1.01/1.43 , clause( 767, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.43 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.01/1.43 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ] )
% 1.01/1.43 , clause( 768, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.01/1.43 ~( =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.43 , clause( 769, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.43 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ] )
% 1.01/1.43 , clause( 770, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.43 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.01/1.43 ) ) ] )
% 1.01/1.43 , clause( 771, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.43 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.01/1.43 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.01/1.43 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.43 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.01/1.43 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.43 ) ] )
% 1.01/1.43 , clause( 772, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.01/1.43 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.43 X ), X ) ) ] )
% 1.01/1.43 , clause( 773, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.01/1.43 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.43 X ), X ) ) ] )
% 1.01/1.43 , clause( 774, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.43 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.01/1.44 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.44 X ), X ) ) ] )
% 1.01/1.44 , clause( 775, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.01/1.44 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.44 X ), X ) ) ] )
% 1.01/1.44 , clause( 776, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 Y, Y, X ) ) ] )
% 1.01/1.44 , clause( 777, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 778, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.01/1.44 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 779, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.01/1.44 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 780, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T
% 1.01/1.44 , X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.01/1.44 X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 781, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 782, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.01/1.44 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 1.01/1.44 , clause( 783, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.01/1.44 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 784, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.01/1.44 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.01/1.44 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 785, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 786, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 1.01/1.44 , clause( 787, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.01/1.44 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 Y, T, X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 788, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.01/1.44 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 Y, T, X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 789, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 790, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y,
% 1.01/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 1.01/1.44 ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 1.01/1.44 , clause( 791, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 1.01/1.44 , clause( 792, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y,
% 1.01/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 1.01/1.44 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 793, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.01/1.44 X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 794, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.01/1.44 X ), X ), Y ) ] )
% 1.01/1.44 , clause( 795, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 796, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 797, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 798, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 799, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.01/1.44 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.01/1.44 X ), X ), X ) ] )
% 1.01/1.44 , clause( 800, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.01/1.44 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 801, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 1.01/1.44 Z, Y, X ) ) ] )
% 1.01/1.44 , clause( 802, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ] )
% 1.01/1.44 , clause( 803, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.44 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), Z, X ) ), =( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 804, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.44 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), T, X ) ), =( T,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 805, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 1.01/1.44 X ), X ) ) ] )
% 1.01/1.44 , clause( 806, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 807, [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 808, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 809, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 810, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 811, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.44 Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 812, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.44 Z, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 813, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.01/1.44 , X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 814, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.01/1.44 , X ), Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 815, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 816, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 1.01/1.44 , clause( 817, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 818, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 819, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T
% 1.01/1.44 , X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.01/1.44 X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 820, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 821, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.01/1.44 'c_lessequals'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 822, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.01/1.44 'c_lessequals'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 823, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.01/1.44 , X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 1.01/1.44 , clause( 824, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.01/1.44 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 1.01/1.44 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 1.01/1.44 , clause( 825, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) )
% 1.01/1.44 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 Y, T, X ) ) ), =( Z, T ) ] )
% 1.01/1.44 , clause( 826, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 1.01/1.44 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 Y, T, X ) ) ), =( Z, T ) ] )
% 1.01/1.44 , clause( 827, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 1.01/1.44 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 T, Z, X ) ) ), =( Y, T ) ] )
% 1.01/1.44 , clause( 828, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 829, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 830, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 831, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 832, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 833, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 834, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 835, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 836, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 837, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.01/1.44 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 838, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.01/1.44 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 839, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 1.01/1.44 , clause( 840, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ] )
% 1.01/1.44 , clause( 841, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.44 Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 842, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 1.01/1.44 , clause( 843, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 844, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 1.01/1.44 , clause( 845, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 846, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.01/1.44 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 847, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.01/1.44 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 848, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 1.01/1.44 , clause( 849, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 850, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_OscaleR__class_OscaleR'( Y, Z
% 1.01/1.44 , X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 851, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_OscaleR__class_OscaleR'( Y, Z
% 1.01/1.44 , X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 852, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_RealVector_OscaleR__class_OscaleR'( Z
% 1.01/1.44 , T, X ), X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 853, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_RealVector_OscaleR__class_OscaleR'( Z
% 1.01/1.44 , T, X ), X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 854, [ ~( 'class_RealVector_Oreal__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_OscaleR__class_OscaleR'( Y, Z
% 1.01/1.44 , X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 855, [ ~( 'class_RealVector_Oreal__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_RealVector_OscaleR__class_OscaleR'( Z
% 1.01/1.44 , T, X ), X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 856, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 857, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 858, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 859, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.01/1.44 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 860, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.44 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 1.01/1.44 , clause( 861, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 862, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 863, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.44 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 864, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.44 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 865, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 866, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.01/1.44 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 1.01/1.44 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 867, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ] )
% 1.01/1.44 , clause( 868, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.01/1.44 , T, X ), X ) ) ] )
% 1.01/1.44 , clause( 869, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.01/1.44 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 870, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.01/1.44 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 871, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.01/1.44 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 872, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 T, 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z, X ), W, X ), X ) ) ] )
% 1.01/1.44 , clause( 873, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.44 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 1.01/1.44 , X ), W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 874, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W, X ) ) ] )
% 1.01/1.44 , clause( 875, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ] )
% 1.01/1.44 , clause( 876, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.44 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.01/1.44 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 877, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.44 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.01/1.44 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 878, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.01/1.44 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 1.01/1.44 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 1.01/1.44 , clause( 879, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.01/1.44 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.01/1.44 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 880, [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.44 Z, X ), X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 881, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.44 Z, X ), X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 882, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 1.01/1.44 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 1.01/1.44 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 883, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.01/1.44 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 1.01/1.44 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 884, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 885, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.01/1.44 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 886, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.01/1.44 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 887, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.01/1.44 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 888, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ] )
% 1.01/1.44 , clause( 889, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ] )
% 1.01/1.44 , clause( 890, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 891, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.01/1.44 , X ), X ) ) ] )
% 1.01/1.44 , clause( 892, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 893, [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.44 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.01/1.44 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ] )
% 1.01/1.44 , clause( 894, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 895, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.44 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.44 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 896, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 897, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 898, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 899, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.01/1.44 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 900, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.01/1.44 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 901, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.01/1.44 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 902, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ] )
% 1.01/1.44 , clause( 903, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ] )
% 1.01/1.44 , clause( 904, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T,
% 1.01/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 905, [ =( 'c_RealVector_Onorm__class_Onorm'( 'c_Complex_Ocnj'( X
% 1.01/1.44 ), 'tc_Complex_Ocomplex' ), 'c_RealVector_Onorm__class_Onorm'( X,
% 1.01/1.44 'tc_Complex_Ocomplex' ) ) ] )
% 1.01/1.44 , clause( 906, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.44 , Y, X ), X ) ] )
% 1.01/1.44 , clause( 907, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.44 , Z, X ), X ) ] )
% 1.01/1.44 , clause( 908, [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.44 , Z, X ), X ) ] )
% 1.01/1.44 , clause( 909, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.01/1.44 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 910, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.44 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 911, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 912, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 913, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 914, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ),
% 1.01/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 915, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.01/1.44 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.44 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 916, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.01/1.44 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.44 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 917, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ] )
% 1.01/1.44 , clause( 918, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.01/1.44 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 919, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.01/1.44 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 920, [ =( 'c_Complex_Ocnj'( 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ) ] )
% 1.01/1.44 , clause( 921, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.01/1.44 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.01/1.44 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 922, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.44 , Y, X ) ) ] )
% 1.01/1.44 , clause( 923, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.44 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 924, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.44 , Y, X ) ) ] )
% 1.01/1.44 , clause( 925, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.44 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.01/1.44 , T, X ), X ), T, X ) ) ] )
% 1.01/1.44 , clause( 926, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.01/1.44 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 1.01/1.44 , clause( 927, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 1.01/1.44 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 928, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 929, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.44 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 930, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.01/1.44 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 931, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.44 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 932, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.44 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 933, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.01/1.44 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 934, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.44 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 935, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.01/1.44 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 936, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.44 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 937, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.01/1.44 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 938, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.01/1.44 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ] )
% 1.01/1.44 , clause( 939, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.01/1.44 X ) ] )
% 1.01/1.44 , clause( 940, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'(
% 1.01/1.44 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 1.01/1.44 , clause( 941, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 1.01/1.44 , clause( 942, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 1.01/1.44 Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.01/1.44 , clause( 943, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 1.01/1.44 , clause( 944, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 945, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 1.01/1.44 , clause( 946, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 1.01/1.44 , clause( 947, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 1.01/1.44 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 1.01/1.44 , clause( 948, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.44 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 1.01/1.44 , clause( 949, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.01/1.44 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 1.01/1.44 , clause( 950, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 951, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 952, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 953, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 954, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.01/1.44 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 955, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.01/1.44 X ), X ), Y ) ] )
% 1.01/1.44 , clause( 956, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.44 ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.01/1.44 , T, X ), X ) ) ] )
% 1.01/1.44 , clause( 957, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.44 ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.44 , Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 958, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 1.01/1.44 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 959, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.44 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.44 X ), T, X ) ) ] )
% 1.01/1.44 , clause( 960, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 1.01/1.44 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 961, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.44 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 962, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 963, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 964, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.01/1.44 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 965, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_RealVector_OscaleR__class_OscaleR'( Y
% 1.01/1.44 , Z, X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 966, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 1.01/1.44 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.01/1.44 ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 967, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 1.01/1.44 , clause( 968, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 969, [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.44 , U, X ), X ), W, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Z, U, X ), W, X ), X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, T, X ), W, X ), U, X ), X ) ) ] )
% 1.01/1.44 , clause( 970, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.01/1.44 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 971, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ] )
% 1.01/1.44 , clause( 972, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.01/1.44 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X
% 1.01/1.44 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 973, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.44 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 1.01/1.44 , clause( 974, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.01/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 975, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 976, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 977, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.44 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 1.01/1.44 , clause( 978, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.01/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 979, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 980, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 981, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.01/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 1.01/1.44 , clause( 982, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.01/1.44 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ] )
% 1.01/1.44 , clause( 983, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.01/1.44 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 984, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X )
% 1.01/1.44 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 1.01/1.44 , clause( 985, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.01/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.01/1.44 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 1.01/1.44 , clause( 986, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.01/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.01/1.44 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.01/1.44 , X ), W, X ) ) ] )
% 1.01/1.44 , clause( 987, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 988, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.44 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.01/1.44 , X ), 'c_RealVector_Onorm__class_Onorm'( Y, X ) ) ] )
% 1.01/1.44 , clause( 989, [ =( 'c_Complex_Ocnj'( 'c_Complex_Ocnj'( X ) ), X ) ] )
% 1.01/1.44 , clause( 990, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Z, T, X ), X ),
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 991, [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Z, T, X ), X ),
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 992, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Z, T, X ), X ),
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 993, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 994, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 995, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 996, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 997, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 998, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 999, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 1000, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 1001, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 1002, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.01/1.44 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1003, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.01/1.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.01/1.44 , T, X ), X ), T, X ) ) ] )
% 1.01/1.44 , clause( 1004, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , Z, X ), 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 1005, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X )
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1006, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X )
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1007, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 1.01/1.44 T, X ) ) ] )
% 1.01/1.44 , clause( 1008, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.01/1.44 T, X ) ) ] )
% 1.01/1.44 , clause( 1009, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 1.01/1.44 T, X ) ) ] )
% 1.01/1.44 , clause( 1010, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.01/1.44 T, X ) ) ] )
% 1.01/1.44 , clause( 1011, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X )
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1012, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X )
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1013, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.01/1.44 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.44 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.01/1.44 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.01/1.44 , Y, X ) ) ] )
% 1.01/1.44 , clause( 1014, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.01/1.44 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 , Z, X ) ] )
% 1.01/1.44 , clause( 1015, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.01/1.44 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.01/1.44 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 , Z, X ) ] )
% 1.01/1.44 , clause( 1016, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.01/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.01/1.44 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.44 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 1017, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.01/1.44 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.44 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ),
% 1.01/1.44 ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 1018, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.01/1.44 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 , T, X ) ] )
% 1.01/1.44 , clause( 1019, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.01/1.44 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 , T, X ) ] )
% 1.01/1.44 , clause( 1020, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.01/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.44 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.01/1.44 Z, X ) ) ] )
% 1.01/1.44 , clause( 1021, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 1.01/1.44 , clause( 1022, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 1.01/1.44 , clause( 1023, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.01/1.44 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 1.01/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 1.01/1.44 W, X ), X ) ) ] )
% 1.01/1.44 , clause( 1024, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.01/1.44 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.01/1.44 , X ), T, X ), W, X ) ) ] )
% 1.01/1.44 , clause( 1025, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 1.01/1.44 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 1.01/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 1.01/1.44 W, X ), X ) ) ] )
% 1.01/1.44 , clause( 1026, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.01/1.44 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.01/1.44 , X ), W, X ), X ) ) ] )
% 1.01/1.44 , clause( 1027, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , Z, X ), 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 1028, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1029, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.01/1.44 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 1.01/1.44 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 1.01/1.44 Z, X ) ) ] )
% 1.01/1.44 , clause( 1030, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1031, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1032, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1033, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1034, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1035, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1036, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1037, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1038, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Y, T, X
% 1.01/1.44 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( T, Z
% 1.01/1.44 , X ), X ) ) ] )
% 1.01/1.44 , clause( 1039, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.01/1.44 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ] )
% 1.01/1.44 , clause( 1040, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.01/1.44 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ] )
% 1.01/1.44 , clause( 1041, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 1042, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.01/1.44 ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( T, Y, X
% 1.01/1.44 ), Z, X ) ) ] )
% 1.01/1.44 , clause( 1043, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.01/1.44 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.44 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 1.01/1.44 =( Y, T ) ] )
% 1.01/1.44 , clause( 1044, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.01/1.44 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.44 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 1.01/1.44 =( Y, T ) ] )
% 1.01/1.44 , clause( 1045, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1046, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.01/1.44 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 1.01/1.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 1.01/1.44 X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 1047, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 , X ) ] )
% 1.01/1.44 , clause( 1048, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.44 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1049, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.01/1.44 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1050, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.01/1.44 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1051, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.44 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.01/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1052, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.44 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1053, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1054, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1055, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1056, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1057, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.44 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.01/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1058, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1059, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1060, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 1.01/1.44 ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.01/1.44 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1061, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 1.01/1.44 ) ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1062, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 1063, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.44 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.44 Y, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 1064, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.01/1.44 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.44 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ] )
% 1.01/1.44 , clause( 1065, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 1066, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 1067, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 1.01/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1068, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 1.01/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 1069, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 1.01/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1070, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 1.01/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 1071, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 1.01/1.44 Z, Y, X ) ) ] )
% 1.01/1.44 , clause( 1072, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1073, [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1074, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.01/1.44 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 1.01/1.44 , clause( 1075, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.01/1.44 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1076, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.01/1.44 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1077, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.01/1.44 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1078, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.01/1.44 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1079, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.01/1.44 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1080, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.44 X ), X ) ) ] )
% 1.01/1.44 , clause( 1081, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.44 X ), X ) ) ] )
% 1.01/1.44 , clause( 1082, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.01/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1083, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1084, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.01/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1085, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.01/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1086, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 1.01/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 1.01/1.44 , clause( 1087, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 1.01/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1088, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 1089, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1090, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 1.01/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 1.01/1.44 , clause( 1091, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 1.01/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1092, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 1.01/1.44 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 1093, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.01/1.44 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 1094, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 1095, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.01/1.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 1.01/1.44 , clause( 1096, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.01/1.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 1.01/1.44 , clause( 1097, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1098, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1099, [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.01/1.44 T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1100, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.01/1.44 T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1101, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1102, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1103, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1104, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1105, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.44 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ] )
% 1.01/1.44 , clause( 1106, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.44 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1107, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.44 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1108, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.01/1.44 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 Y, T, X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 1109, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.44 Y, X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1110, [ ~(
% 1.01/1.44 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 1.01/1.44 , clause( 1111, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1112, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 1113, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.44 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.44 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1114, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 1.01/1.44 , clause( 1115, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1116, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 1117, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.44 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.44 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 1.01/1.44 , clause( 1118, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 1.01/1.44 , clause( 1119, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 1120, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.44 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.44 X ), T, X ) ) ] )
% 1.01/1.44 , clause( 1121, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1122, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.44 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1123, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.01/1.44 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1124, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 1.01/1.44 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1125, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.01/1.44 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 1126, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 1127, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1128, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.01/1.44 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1129, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.01/1.44 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 1130, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 1131, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 1132, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 1133, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.01/1.44 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1134, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.44 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1135, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 1136, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.44 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1137, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.44 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1138, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 1139, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 1.01/1.44 , clause( 1140, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 1141, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 1142, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 1.01/1.44 , clause( 1143, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 1144, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.01/1.44 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.01/1.44 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1145, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.01/1.44 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.01/1.44 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1146, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.44 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.01/1.44 , Y, X ) ) ] )
% 1.01/1.44 , clause( 1147, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.01/1.44 ), Y ) ] )
% 1.01/1.44 , clause( 1148, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 1149, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 1150, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.01/1.44 ), Y ) ] )
% 1.01/1.44 , clause( 1151, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.01/1.44 ), Y ) ] )
% 1.01/1.44 , clause( 1152, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.01/1.44 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1153, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1154, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X
% 1.01/1.44 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X )
% 1.01/1.44 , Y, X ) ) ] )
% 1.01/1.44 , clause( 1155, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X
% 1.01/1.44 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X )
% 1.01/1.44 , Y, X ) ) ] )
% 1.01/1.44 , clause( 1156, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X
% 1.01/1.44 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 1157, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X
% 1.01/1.44 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 1158, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 1159, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 1160, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.01/1.44 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 1.01/1.44 , clause( 1161, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.01/1.44 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 1.01/1.44 , clause( 1162, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 1.01/1.44 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 1163, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.44 Z, X ) ) ] )
% 1.01/1.44 , clause( 1164, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.44 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 1165, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 1166, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.01/1.44 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 1167, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.01/1.44 , clause( 1168, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.01/1.44 , clause( 1169, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.01/1.44 , clause( 1170, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 1.01/1.44 'c_lessequals'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 1171, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.01/1.44 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 1172, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 1173, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1174, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1175, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 1.01/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 1176, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 1177, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ] )
% 1.01/1.44 , clause( 1178, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ] )
% 1.01/1.44 , clause( 1179, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.44 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.01/1.44 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 1180, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.01/1.44 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.01/1.44 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1181, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.44 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.01/1.44 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.01/1.44 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 1182, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1183, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1184, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1185, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 1.01/1.44 , clause( 1186, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 1.01/1.44 , clause( 1187, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1188, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.44 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.44 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1189, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.01/1.44 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.01/1.44 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.01/1.44 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1190, [ ~( =( 'c_Complex_Ocnj'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ) ] )
% 1.01/1.44 , clause( 1191, [ ~( =( 'c_Complex_Ocnj'( X ), 'c_Complex_Ocnj'( Y ) ) ),
% 1.01/1.44 =( X, Y ) ] )
% 1.01/1.44 , clause( 1192, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.01/1.44 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.01/1.44 X ), X ) ) ] )
% 1.01/1.44 , clause( 1193, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.01/1.44 X ) ] )
% 1.01/1.44 , clause( 1194, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1195, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.01/1.44 =( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1196, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 1.01/1.44 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ] )
% 1.01/1.44 , clause( 1197, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1198, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1199, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.01/1.44 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 1.01/1.44 , clause( 1200, [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 1.01/1.44 , clause( 1201, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.01/1.44 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1202, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.01/1.44 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 1203, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 1204, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 1.01/1.44 , clause( 1205, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.01/1.44 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1206, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.01/1.44 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 1.01/1.44 , clause( 1207, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), ~( =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.44 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1208, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1209, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1210, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 1211, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.01/1.44 , clause( 1212, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1213, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.01/1.44 X ), X ) ) ] )
% 1.01/1.44 , clause( 1214, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 Z, T, X ) ) ] )
% 1.01/1.44 , clause( 1215, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 Z, T, X ) ) ] )
% 1.01/1.44 , clause( 1216, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.01/1.44 X ), X ) ) ] )
% 1.01/1.44 , clause( 1217, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1218, [ ~(
% 1.01/1.44 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1219, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , Y, X ) ] )
% 1.01/1.44 , clause( 1220, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y
% 1.01/1.44 , X ) ] )
% 1.01/1.44 , clause( 1221, [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~(
% 1.01/1.44 'c_lessequals'( Z, Y, 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( X, Z,
% 1.01/1.44 'tc_RealDef_Oreal' ) ) ] )
% 1.01/1.44 , clause( 1222, [ 'c_lessequals'( X, X, 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1223, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 1.01/1.44 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1224, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.01/1.44 , clause( 1225, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 1.01/1.44 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ] )
% 1.01/1.44 , clause( 1226, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 1227, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.01/1.44 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1228, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.01/1.44 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 1.01/1.44 , clause( 1229, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 1.01/1.44 , clause( 1230, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 1.01/1.44 , X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1231, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.01/1.44 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1232, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.01/1.44 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1233, [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 , X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1234, [ ~( 'class_RealVector_Oreal__vector'( X ) ), ~( =(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( T, Z, X ) ) ), =( Z,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, T ) ] )
% 1.01/1.44 , clause( 1235, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.01/1.44 ) ) ] )
% 1.01/1.44 , clause( 1236, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.44 , Y, X ), X ) ) ] )
% 1.01/1.44 , clause( 1237, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.44 , T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1238, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.01/1.44 , T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1239, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.44 , Y, X ), X ) ) ] )
% 1.01/1.44 , clause( 1240, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.01/1.44 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ] )
% 1.01/1.44 , clause( 1241, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1242, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.01/1.44 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.01/1.44 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.01/1.44 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ] )
% 1.01/1.44 , clause( 1243, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 1.01/1.44 , clause( 1244, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.01/1.44 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.01/1.44 , clause( 1245, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ] )
% 1.01/1.44 , clause( 1246, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.01/1.44 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.01/1.44 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ] )
% 1.01/1.44 , clause( 1247, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1248, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 1.01/1.44 , X ) ) ] )
% 1.01/1.44 , clause( 1249, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1250, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.01/1.44 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 1251, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 1.01/1.44 , clause( 1252, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1253, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.01/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ] )
% 1.01/1.44 , clause( 1254, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.01/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 1.01/1.44 , clause( 1255, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.01/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.01/1.44 , clause( 1256, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.44 Y, X ) ) ] )
% 1.01/1.44 , clause( 1257, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.44 Y, X ) ) ] )
% 1.01/1.44 , clause( 1258, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.01/1.44 , Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 1.01/1.44 , clause( 1259, [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ),
% 1.01/1.44 'c_lessequals'( Y, X, 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1260, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.44 Y, X ) ) ] )
% 1.01/1.44 , clause( 1261, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 1.01/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.01/1.44 Y, X ) ) ] )
% 1.01/1.44 , clause( 1262, [ =( 'c_Polynomial_Opoly'( 'v_q____',
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( X, 'v_c____', 'tc_Complex_Ocomplex' ),
% 1.01/1.44 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_pa____', X,
% 1.01/1.44 'tc_Complex_Ocomplex' ) ) ] )
% 1.01/1.44 , clause( 1263, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1264, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.01/1.44 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.01/1.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.01/1.44 X ), Z, X ) ) ] )
% 1.01/1.44 , clause( 1265, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.01/1.44 X ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.44 Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1266, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.01/1.44 =( 'c_Polynomial_Opoly'( 'c_Polynomial_Opcompose'( Y, Z, X ), T, X ),
% 1.01/1.44 'c_Polynomial_Opoly'( Y, 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1267, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.01/1.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 1.01/1.44 , clause( 1268, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.01/1.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 1.01/1.44 , clause( 1269, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.01/1.44 X ), T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.44 Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1270, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.01/1.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.01/1.44 , T, X ), X ), T, X ) ) ] )
% 1.01/1.44 , clause( 1271, [ =( 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'(
% 1.01/1.44 'v_q____', 'tc_Complex_Ocomplex' ),
% 1.01/1.44 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( 'v_pa____',
% 1.01/1.44 'tc_Complex_Ocomplex' ) ) ] )
% 1.01/1.44 , clause( 1272, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X
% 1.01/1.44 ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.01/1.44 ), X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X
% 1.01/1.44 ), X ) ) ] )
% 1.01/1.44 , clause( 1273, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 1.01/1.44 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 1.01/1.44 , clause( 1274, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 1.01/1.44 ~( 'c_lessequals'( U, T, X ) ) ] )
% 1.01/1.44 , clause( 1275, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 1.01/1.44 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 1276, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.01/1.44 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 1.01/1.44 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 1.01/1.44 , clause( 1277, [ ~( =( 'c_Polynomial_Opoly'( 'v_pa____', 'v_c____',
% 1.01/1.44 'tc_Complex_Ocomplex' ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ) ), =( 'c_Polynomial_Opoly'( 'v_pa____',
% 1.01/1.44 'v_sko__unknown__thm__rrB__1'( 'v_pa____' ), 'tc_Complex_Ocomplex' ),
% 1.01/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ] )
% 1.01/1.44 , clause( 1278, [ =( 'c_Complex_Ocnj'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.01/1.44 'tc_Complex_Ocomplex' ) ), 'c_HOL_Ominus__class_Ominus'( 'c_Complex_Ocnj'(
% 1.01/1.44 X ), 'c_Complex_Ocnj'( Y ), 'tc_Complex_Ocomplex' ) ) ] )
% 1.01/1.44 , clause( 1279, [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.01/1.44 , T, X ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1280, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.01/1.44 , T, X ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 1.01/1.44 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1281, [ 'c_lessequals'( 'c_RealVector_Onorm__class_Onorm'(
% 1.01/1.44 'c_Polynomial_Opoly'( 'v_pa____', 'v_c____', 'tc_Complex_Ocomplex' ),
% 1.01/1.44 'tc_Complex_Ocomplex' ), 'c_RealVector_Onorm__class_Onorm'(
% 1.01/1.44 'c_Polynomial_Opoly'( 'v_pa____', X, 'tc_Complex_Ocomplex' ),
% 1.01/1.44 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1282, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.01/1.44 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.44 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1283, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.01/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.01/1.44 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.01/1.44 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1284, [ =( 'c_Polynomial_Opoly'( 'v_q____', X,
% 1.01/1.44 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_pa____',
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'v_c____', X, 'tc_Complex_Ocomplex' ),
% 1.01/1.44 'tc_Complex_Ocomplex' ) ) ] )
% 1.01/1.44 , clause( 1285, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.01/1.44 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.01/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.01/1.44 , clause( 1286, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1287, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1288, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1289, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1290, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.01/1.44 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 1.01/1.44 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.01/1.44 , clause( 1291, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 1.01/1.44 ), Y ) ] )
% 1.01/1.44 , clause( 1292, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.01/1.44 , T, X ) ) ), =( Z, T ) ] )
% 1.01/1.44 , clause( 1293, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.01/1.44 , T, X ) ) ), =( Y, Z ) ] )
% 1.01/1.44 , clause( 1294, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 ) ), =( Y, Z ) ] )
% 1.01/1.44 , clause( 1295, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.01/1.44 ) ), =( Y, Z ) ] )
% 1.01/1.44 , clause( 1296, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.01/1.44 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.01/1.44 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 1.01/1.44 , clause( 1297, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.01/1.44 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.44 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1298, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.01/1.44 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.01/1.44 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1299, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.01/1.44 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.01/1.44 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1300, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.01/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.01/1.44 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.01/1.44 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.01/1.44 , clause( 1301, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.01/1.44 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.01/1.44 , U, X ), X ) ) ] )
% 1.01/1.44 , clause( 1302, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 1.01/1.44 'c_Polynomial_Opoly'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.44 'c_Polynomial_Opoly'( Y, T, X ), 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1303, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.01/1.44 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.01/1.44 ), X ), 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'(
% 1.01/1.44 Z, Y, X ), X ) ) ] )
% 1.01/1.44 , clause( 1304, [ ~( =( 'c_Polynomial_Opoly'( 'v_pa____', 'v_c____',
% 1.01/1.44 'tc_Complex_Ocomplex' ), 'c_HOL_Ozero__class_Ozero'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ) ) ] )
% 1.01/1.44 , clause( 1305, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.01/1.44 ), Y ) ] )
% 1.01/1.44 , clause( 1306, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.01/1.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.01/1.44 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ] )
% 1.01/1.44 , clause( 1307, [ =( 'c_Polynomial_Opoly'( 'v_q____',
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( X, 'v_c____', 'tc_Complex_Ocomplex' ),
% 1.01/1.44 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_pa____', X,
% 1.01/1.44 'tc_Complex_Ocomplex' ) ) ] )
% 1.01/1.44 , clause( 1308, [ ~( =( 'c_Polynomial_Opoly'( 'v_pa____', 'v_x____',
% 1.01/1.44 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_q____',
% 1.01/1.44 'c_HOL_Ominus__class_Ominus'( 'v_x____', 'v_c____', 'tc_Complex_Ocomplex'
% 1.01/1.44 ), 'tc_Complex_Ocomplex' ) ) ) ] )
% 1.01/1.44 , clause( 1309, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.44 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 1.01/1.44 , clause( 1310, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1311, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1312, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_nat'
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1313, [
% 1.01/1.44 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1314, [
% 1.01/1.44 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1315, [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.01/1.44 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1316, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.01/1.44 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1317, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.01/1.44 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1318, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 1.01/1.44 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1319, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 1.01/1.44 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1320, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.01/1.44 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1321, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 1322, [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 1323, [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1324, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 1325, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1326, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1327, [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1328, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1329, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1330, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1331, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1332, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1333, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1334, [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1335, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1336, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1337, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1338, [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1339, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1340, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1341, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 1.01/1.44 , clause( 1342, [
% 1.01/1.44 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1343, [
% 1.01/1.44 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1344, [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1345, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1346, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1347, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1348, [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1349, [ 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1350, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1351, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1352, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1353, [ 'class_Ring__and__Field_Oordered__ring__strict'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1354, [ 'class_OrderedGroup_Opordered__ab__group__add'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1355, [ 'class_OrderedGroup_Olordered__ab__group__add'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1356, [ 'class_OrderedGroup_Oordered__ab__group__add'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1357, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1358, [ 'class_Ring__and__Field_Opordered__semiring'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1359, [ 'class_Ring__and__Field_Opordered__ring__abs'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1360, [ 'class_Ring__and__Field_Oordered__semiring'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1361, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1362, [ 'class_Ring__and__Field_Odivision__by__zero'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1363, [ 'class_Ring__and__Field_Oordered__semidom'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1364, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1365, [ 'class_Ring__and__Field_Ocomm__semiring__0'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1366, [ 'class_RealVector_Oreal__normed__algebra'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1367, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1368, [ 'class_RealVector_Oreal__normed__vector'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1369, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1370, [ 'class_Ring__and__Field_Opordered__ring'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1371, [ 'class_Ring__and__Field_Oordered__field'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1372, [ 'class_Ring__and__Field_Olordered__ring'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1373, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1374, [ 'class_RealVector_Oreal__normed__field'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1375, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1376, [ 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1377, [ 'class_Ring__and__Field_Ocomm__ring__1'(
% 1.01/1.44 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1378, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_RealDef_Oreal'
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1379, [ 'class_OrderedGroup_Oab__group__add'( 'tc_RealDef_Oreal'
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1380, [ 'class_Ring__and__Field_Omult__zero'( 'tc_RealDef_Oreal'
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1381, [ 'class_Ring__and__Field_Omult__mono'( 'tc_RealDef_Oreal'
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1382, [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_RealDef_Oreal'
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1383, [ 'class_Ring__and__Field_Osemiring'( 'tc_RealDef_Oreal' )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 1384, [ 'class_RealVector_Oreal__algebra'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1385, [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1386, [ 'class_RealVector_Oreal__vector'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1387, [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1388, [ 'class_Ring__and__Field_Oabs__if'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1389, [ 'class_RealVector_Oreal__field'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1390, [ 'class_Ring__and__Field_Ofield'( 'tc_RealDef_Oreal' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1391, [ 'class_Ring__and__Field_Oring'( 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1392, [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1393, [ 'class_Ring__and__Field_Odvd'( 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1394, [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1395, [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1396, [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1397, [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ] )
% 1.01/1.44 , clause( 1398, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1399, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1400, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1401, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1402, [ 'class_Ring__and__Field_Odivision__by__zero'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1403, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1404, [ 'class_Ring__and__Field_Ocomm__semiring__0'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1405, [ 'class_RealVector_Oreal__normed__algebra'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1406, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1407, [ 'class_RealVector_Oreal__normed__vector'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1408, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1409, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1410, [ 'class_RealVector_Oreal__normed__field'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1411, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1412, [ 'class_Ring__and__Field_Ocomm__ring__1'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1413, [ 'class_OrderedGroup_Oab__group__add'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1414, [ 'class_Ring__and__Field_Omult__zero'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1415, [ 'class_Ring__and__Field_Ocomm__ring'(
% 1.01/1.44 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1416, [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex'
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1417, [ 'class_RealVector_Oreal__algebra'( 'tc_Complex_Ocomplex'
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1418, [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex'
% 1.01/1.44 ) ] )
% 1.01/1.44 , clause( 1419, [ 'class_RealVector_Oreal__vector'( 'tc_Complex_Ocomplex' )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 1420, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 1421, [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 1422, [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' )
% 1.01/1.44 ] )
% 1.01/1.44 , clause( 1423, [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1424, [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1425, [ 'class_Ring__and__Field_Odvd'( 'tc_Complex_Ocomplex' ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1426, [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ] )
% 1.01/1.44 , clause( 1427, [
% 1.01/1.44 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1428, [
% 1.01/1.44 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1429, [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1430, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1431, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1432, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1433, [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1434, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1435, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1436, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.44 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 1.01/1.44 , clause( 1437, [ 'class_Ring__and__Field_Oordered__ring__strict'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1438, [ 'class_OrderedGroup_Opordered__ab__group__add'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1439, [ 'class_OrderedGroup_Oordered__ab__group__add'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1440, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.44 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 1.01/1.44 , clause( 1441, [ 'class_Ring__and__Field_Opordered__semiring'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1442, [ 'class_Ring__and__Field_Opordered__ring__abs'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1443, [ 'class_Ring__and__Field_Oordered__semiring'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1444, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 1.01/1.44 )
% 1.01/1.44 , clause( 1445, [ 'class_Ring__and__Field_Oordered__semidom'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1446, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 1.01/1.44 , clause( 1447, [ 'class_Ring__and__Field_Ocomm__semiring__0'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 1.01/1.44 , clause( 1448, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 1.01/1.44 , clause( 1449, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1450, [ 'class_Ring__and__Field_Opordered__ring'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1451, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.44 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 1.01/1.44 , clause( 1452, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1453, [ 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.44 X ) ) ] )
% 1.01/1.44 , clause( 1454, [ 'class_Ring__and__Field_Ocomm__ring__1'(
% 1.01/1.44 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Ocomm__ring__1'(
% 1.01/1.45 X ) ) ] )
% 1.01/1.45 , clause( 1455, [ 'class_Ring__and__Field_Omult__mono1'(
% 1.01/1.45 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.45 X ) ) ] )
% 1.01/1.45 , clause( 1456, [ 'class_OrderedGroup_Oab__group__add'(
% 1.01/1.45 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Oab__group__add'( X
% 1.01/1.45 ) ) ] )
% 1.01/1.45 , clause( 1457, [ 'class_Ring__and__Field_Omult__zero'(
% 1.01/1.45 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.01/1.45 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 1.01/1.45 , clause( 1458, [ 'class_Ring__and__Field_Omult__mono'(
% 1.01/1.45 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 1.01/1.45 X ) ) ] )
% 1.01/1.45 , clause( 1459, [ 'class_Ring__and__Field_Ocomm__ring'(
% 1.01/1.45 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Ocomm__ring'( X
% 1.01/1.45 ) ) ] )
% 1.01/1.45 , clause( 1460, [ 'class_Ring__and__Field_Osemiring'( 'tc_Polynomial_Opoly'(
% 1.01/1.45 X ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 1.01/1.45 , clause( 1461, [ 'class_OrderedGroup_Omonoid__add'( 'tc_Polynomial_Opoly'(
% 1.01/1.45 X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ] )
% 1.01/1.45 , clause( 1462, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Polynomial_Opoly'(
% 1.01/1.45 X ) ), ~( 'class_OrderedGroup_Oab__group__add'( X ) ) ] )
% 1.01/1.45 , clause( 1463, [ 'class_Ring__and__Field_Oabs__if'( 'tc_Polynomial_Opoly'(
% 1.01/1.45 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.01/1.45 , clause( 1464, [ 'class_Divides_Osemiring__div'( 'tc_Polynomial_Opoly'( X
% 1.01/1.45 ) ), ~( 'class_Ring__and__Field_Ofield'( X ) ) ] )
% 1.01/1.45 , clause( 1465, [ 'class_Ring__and__Field_Oring'( 'tc_Polynomial_Opoly'( X
% 1.01/1.45 ) ), ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ) ] )
% 1.01/1.45 , clause( 1466, [ 'class_Ring__and__Field_Oidom'( 'tc_Polynomial_Opoly'( X
% 1.01/1.45 ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ] )
% 1.01/1.45 , clause( 1467, [ 'class_Ring__and__Field_Odvd'( 'tc_Polynomial_Opoly'( X )
% 1.01/1.45 ), ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 1.01/1.45 , clause( 1468, [ 'class_Orderings_Opreorder'( 'tc_Polynomial_Opoly'( X ) )
% 1.01/1.45 , ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.01/1.45 , clause( 1469, [ 'class_Orderings_Olinorder'( 'tc_Polynomial_Opoly'( X ) )
% 1.01/1.45 , ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.01/1.45 , clause( 1470, [ 'class_Divides_Oring__div'( 'tc_Polynomial_Opoly'( X ) )
% 1.01/1.45 , ~( 'class_Ring__and__Field_Ofield'( X ) ) ] )
% 1.01/1.45 , clause( 1471, [ 'class_Orderings_Oorder'( 'tc_Polynomial_Opoly'( X ) ),
% 1.01/1.45 ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 1.01/1.45 , clause( 1472, [ 'class_Int_Onumber__ring'( 'tc_Polynomial_Opoly'( X ) ),
% 1.01/1.45 ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ] )
% 1.01/1.45 ] ).
% 1.01/1.45
% 1.01/1.45
% 1.01/1.45
% 1.01/1.45 subsumption(
% 1.01/1.45 clause( 563, [ =( 'c_Polynomial_Opoly'( 'v_q____',
% 1.01/1.45 'c_HOL_Ominus__class_Ominus'( X, 'v_c____', 'tc_Complex_Ocomplex' ),
% 1.01/1.45 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_pa____', X,
% 1.01/1.45 'tc_Complex_Ocomplex' ) ) ] )
% 1.01/1.45 , clause( 1262, [ =( 'c_Polynomial_Opoly'( 'v_q____',
% 1.01/1.45 'c_HOL_Ominus__class_Ominus'( X, 'v_c____', 'tc_Complex_Ocomplex' ),
% 1.01/1.45 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_pa____', X,
% 1.01/1.45 'tc_Complex_Ocomplex' ) ) ] )
% 1.01/1.45 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.01/1.45
% 1.01/1.45
% 1.01/1.45 paramod(
% 1.01/1.45 clause( 3538, [ ~( =( 'c_Polynomial_Opoly'( 'v_pa____', 'v_x____',
% 1.01/1.45 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_pa____', 'v_x____',
% 1.01/1.45 'tc_Complex_Ocomplex' ) ) ) ] )
% 1.01/1.45 , clause( 563, [ =( 'c_Polynomial_Opoly'( 'v_q____',
% 1.01/1.45 'c_HOL_Ominus__class_Ominus'( X, 'v_c____', 'tc_Complex_Ocomplex' ),
% 1.01/1.45 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_pa____', X,
% 1.01/1.45 'tc_Complex_Ocomplex' ) ) ] )
% 1.01/1.45 , 0, clause( 1308, [ ~( =( 'c_Polynomial_Opoly'( 'v_pa____', 'v_x____',
% 1.01/1.45 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_q____',
% 1.01/1.45 'c_HOL_Ominus__class_Ominus'( 'v_x____', 'v_c____', 'tc_Complex_Ocomplex'
% 1.01/1.45 ), 'tc_Complex_Ocomplex' ) ) ) ] )
% 1.01/1.45 , 0, 6, substitution( 0, [ :=( X, 'v_x____' )] ), substitution( 1, [] )
% 1.01/1.45 ).
% 1.01/1.45
% 1.01/1.45
% 1.01/1.45 eqrefl(
% 1.01/1.45 clause( 3539, [] )
% 1.01/1.45 , clause( 3538, [ ~( =( 'c_Polynomial_Opoly'( 'v_pa____', 'v_x____',
% 1.01/1.45 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_pa____', 'v_x____',
% 1.01/1.45 'tc_Complex_Ocomplex' ) ) ) ] )
% 1.01/1.45 , 0, substitution( 0, [] )).
% 1.01/1.45
% 1.01/1.45
% 1.01/1.45 subsumption(
% 1.01/1.45 clause( 598, [] )
% 1.01/1.45 , clause( 3539, [] )
% 1.01/1.45 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.01/1.45
% 1.01/1.45
% 1.01/1.45 end.
% 1.01/1.45
% 1.01/1.45 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.01/1.45
% 1.01/1.45 Memory use:
% 1.01/1.45
% 1.01/1.45 space for terms: 46937
% 1.01/1.45 space for clauses: 48062
% 1.01/1.45
% 1.01/1.45
% 1.01/1.45 clauses generated: 709
% 1.01/1.45 clauses kept: 599
% 1.01/1.45 clauses selected: 0
% 1.01/1.45 clauses deleted: 0
% 1.01/1.45 clauses inuse deleted: 0
% 1.01/1.45
% 1.01/1.45 subsentry: 10043
% 1.01/1.45 literals s-matched: 4621
% 1.01/1.45 literals matched: 4519
% 1.01/1.45 full subsumption: 1020
% 1.01/1.45
% 1.01/1.45 checksum: -1494053691
% 1.01/1.45
% 1.01/1.45
% 1.01/1.45 Bliksem ended
%------------------------------------------------------------------------------