TSTP Solution File: ALG353-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG353-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 12:10:27 EDT 2022
% Result : Unsatisfiable 2.31s 2.67s
% Output : Refutation 2.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG353-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Thu Jun 9 06:56:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.87/1.27 *** allocated 10000 integers for termspace/termends
% 0.87/1.27 *** allocated 10000 integers for clauses
% 0.87/1.27 *** allocated 10000 integers for justifications
% 0.87/1.27 *** allocated 15000 integers for termspace/termends
% 0.87/1.27 Bliksem 1.12
% 0.87/1.27
% 0.87/1.27
% 0.87/1.27 Automatic Strategy Selection
% 0.87/1.27
% 0.87/1.27 Clauses:
% 0.87/1.27 [
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.27 , Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.27 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.27 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.27 [ ~( =( 'c_Complex_Ocomplex_OComplex'( X, Y ), 'c_HOL_Oone__class_Oone'(
% 0.87/1.27 'tc_Complex_Ocomplex' ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.87/1.27 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 0.87/1.27 [ =( 'c_Complex_ORe'( 'c_HOL_Ouminus__class_Ouminus'( X,
% 0.87/1.27 'tc_Complex_Ocomplex' ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.27 'c_Complex_ORe'( X ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.87/1.27 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.87/1.27 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.27 ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.27 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.27 , T, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.27 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.27 , Z, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 0.87/1.27 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.27 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 X ), T, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 0.87/1.27 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.27 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.27 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.27 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.87/1.27 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.87/1.27 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.27 , Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.87/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.27 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 0.87/1.27 ), X ), Y ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 0.87/1.27 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 0.87/1.27 ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 0.87/1.27 [ ~( 'class_RealVector_Oreal__algebra__1'( X ) ), ~( =(
% 0.87/1.27 'c_RealVector_Oof__real'( Y, X ), 'c_RealVector_Oof__real'( Z, X ) ) ),
% 0.87/1.27 =( Y, Z ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.27 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.87/1.27 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~( =(
% 0.87/1.27 'c_RealVector_Onorm__class_Onorm'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 'tc_RealDef_Oreal' ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ =( 'c_Complex_OIm'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.27 'tc_Complex_Ocomplex' ) ), 'c_HOL_Ominus__class_Ominus'( 'c_Complex_OIm'(
% 0.87/1.27 X ), 'c_Complex_OIm'( Y ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.27 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.87/1.27 , 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 'tc_RealDef_Oreal' ) ) ), =( X, Y ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.27 , Z, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.27 , T, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.27 , Z, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.27 , T, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.27 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.87/1.27 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.27 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.27 ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.27 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.27 ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.27 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.27 ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 0.87/1.27 Z, T, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.87/1.27 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 0.87/1.27 ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.87/1.27 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_Complex_Ocomplex' ),
% 0.87/1.27 'c_Complex_Ocomplex_OComplex'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.27 'c_Complex_ORe'( X ), 'c_Complex_ORe'( Y ), 'tc_RealDef_Oreal' ),
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( 'c_Complex_OIm'( X ), 'c_Complex_OIm'( Y ),
% 0.87/1.27 'tc_RealDef_Oreal' ) ) ) ],
% 0.87/1.27 [ ~( 'class_RealVector_Ometric__space'( X ) ), =(
% 0.87/1.27 'c_RealVector_Odist__class_Odist'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.87/1.27 , X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 Z, Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 0.87/1.27 'class_RealVector_Oreal__algebra__1'( X ) ), =( 'c_RealVector_Oof__real'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_RealVector_Oreal__algebra__1'( X ) ), =(
% 0.87/1.27 'c_RealVector_Oof__real'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal'
% 0.87/1.27 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Complex_Ocomplex_OComplex'( X, Y )
% 0.87/1.27 , 'c_Complex_Ocomplex_OComplex'( Z, T ), 'tc_Complex_Ocomplex' ),
% 0.87/1.27 'c_Complex_Ocomplex_OComplex'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 0.87/1.27 'tc_RealDef_Oreal' ), 'c_HOL_Ominus__class_Ominus'( Y, T,
% 0.87/1.27 'tc_RealDef_Oreal' ) ) ) ],
% 0.87/1.27 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_RealVector_Odist__class_Odist'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.27 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.27 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.87/1.27 ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.87/1.27 , X ) ) ), =( Y, Z ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.87/1.27 , X ) ) ), =( Y, Z ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.87/1.27 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.87/1.27 , Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.27 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.27 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.27 ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.27 ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.27 ), =( Z, Y ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.27 , Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.87/1.27 X ), X ) ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' )
% 0.87/1.27 , 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' )
% 0.87/1.27 , ~( 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( X,
% 0.87/1.27 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.27 [ 'c_lessequals'( X, 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.87/1.27 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_RealDef_Oreal' ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 0.87/1.27 ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.27 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.27 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.87/1.27 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.87/1.27 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.87/1.27 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 0.87/1.27 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.87/1.27 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 , X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 , X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.27 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 , X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.87/1.27 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 , X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 0.87/1.27 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.27 'c_NthRoot_Osqrt'( X ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' )
% 0.87/1.27 ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), X,
% 0.87/1.27 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 'tc_RealDef_Oreal' ), 'c_NthRoot_Osqrt'( X ), 'tc_RealDef_Oreal' ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.27 'c_NthRoot_Osqrt'( X ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' )
% 0.87/1.27 ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.27 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.27 [ ~( =( 'c_NthRoot_Osqrt'( X ), 'c_NthRoot_Osqrt'( Y ) ) ), =( X, Y ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 0.87/1.27 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 , X ) ) ],
% 0.87/1.27 [ ~( =( 'c_Complex_Ocomplex_OComplex'( X, Y ),
% 0.87/1.27 'c_Complex_Ocomplex_OComplex'( Z, T ) ) ), =( Y, T ) ],
% 0.87/1.27 [ ~( =( 'c_Complex_Ocomplex_OComplex'( X, Y ),
% 0.87/1.27 'c_Complex_Ocomplex_OComplex'( Z, T ) ) ), =( X, Z ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.87/1.27 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 0.87/1.27 , Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.27 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.87/1.27 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.27 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.87/1.27 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.27 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.87/1.27 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.27 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.27 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.27 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.87/1.27 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.27 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.27 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.87/1.27 ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 0.87/1.27 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.27 'c_RealVector_Odist__class_Odist'( Y, Z, X ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.87/1.27 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.87/1.27 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ouminus__class_Ouminus'( X,
% 0.87/1.27 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 , X ) ) ],
% 0.87/1.27 [ 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.27 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( 'c_NthRoot_Osqrt'( X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 0.87/1.27 ],
% 0.87/1.27 [ 'c_lessequals'( 'c_NthRoot_Osqrt'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( X,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 0.87/1.27 ],
% 0.87/1.27 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~( =(
% 0.87/1.27 'c_RealVector_Odist__class_Odist'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 'tc_RealDef_Oreal' ) ) ), =( Y, Z ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.87/1.27 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.27 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 0.87/1.27 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 0.87/1.27 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ],
% 0.87/1.27 [ =( 'c_RealVector_Onorm__class_Onorm'( 'c_Complex_Ocomplex_OComplex'(
% 0.87/1.27 'c_Transcendental_Ocos'( X ), 'c_Transcendental_Osin'( X ) ),
% 0.87/1.27 'tc_Complex_Ocomplex' ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) )
% 0.87/1.27 ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 0.87/1.27 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 0.87/1.27 ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.27 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.27 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.27 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ ~( 'class_RealVector_Ometric__space'( X ) ), =( Y, Z ), ~(
% 0.87/1.27 'c_lessequals'( 'c_RealVector_Odist__class_Odist'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 0.87/1.27 ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.27 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.27 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.27 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 X ), T, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.27 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal'
% 0.87/1.27 ), Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' ),
% 0.87/1.27 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' ),
% 0.87/1.27 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.27 X, 'tc_RealDef_Oreal' ), Y, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.87/1.27 ), Y ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.87/1.27 ), Y ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.87/1.27 ), Y ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.87/1.27 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 0.87/1.27 , X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.87/1.27 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 0.87/1.27 , X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 0.87/1.27 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.27 , X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 0.87/1.27 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.27 , X ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.27 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.27 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.27 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.87/1.27 , X ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.27 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 0.87/1.27 , X ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.27 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.27 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.27 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.27 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 0.87/1.27 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.27 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.27 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.87/1.27 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.87/1.27 , X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 0.87/1.27 ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.27 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 0.87/1.27 , X ), Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.87/1.27 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.27 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 0.87/1.27 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 0.87/1.27 , X ), 'c_lessequals'( Y, Y, X ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.27 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.27 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.87/1.27 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.87/1.27 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.87/1.27 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.27 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.27 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.87/1.27 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.27 ), X ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.27 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.27 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.27 X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~( 'c_lessequals'( Z,
% 0.87/1.27 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~( 'c_lessequals'( Y,
% 0.87/1.27 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.27 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.27 X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 0.87/1.27 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 0.87/1.27 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.87/1.27 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 Y, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.27 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 Y, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.27 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.87/1.27 X ), X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 Z, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.27 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_RealVector_Oreal__algebra__1'( X ) ), ~( =(
% 0.87/1.27 'c_RealVector_Oof__real'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.87/1.27 =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 0.87/1.28 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.87/1.28 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 0.87/1.28 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.87/1.28 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 0.87/1.28 Y, X ), Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.28 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 0.87/1.28 Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.28 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.28 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.28 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.28 Y, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.87/1.28 [ =( 'c_Complex_OIm'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.28 'tc_Complex_Ocomplex' ) ), 'c_HOL_Oplus__class_Oplus'( 'c_Complex_OIm'( X
% 0.87/1.28 ), 'c_Complex_OIm'( Y ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.28 T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.87/1.28 X ), Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.87/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.87/1.28 T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.28 X ), T, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.87/1.28 T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.28 X ), T, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.28 , X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.87/1.28 , X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.28 , X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 0.87/1.28 , X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 0.87/1.28 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.28 X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 0.87/1.28 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.28 X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.87/1.28 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.28 X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.87/1.28 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.28 X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 Y, Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 Y, Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 0.87/1.28 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 0.87/1.28 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 0.87/1.28 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.28 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.87/1.28 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.87/1.28 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.28 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.87/1.28 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.87/1.28 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__algebra__1'( X ) ), =(
% 0.87/1.28 'c_RealVector_Oof__real'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.87/1.28 'tc_RealDef_Oreal' ), X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.28 'c_RealVector_Oof__real'( Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 0.87/1.28 'class_RealVector_Oreal__algebra__1'( X ) ), =( 'c_RealVector_Oof__real'(
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_RealDef_Oreal' ), X ),
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_RealVector_Oof__real'( Y, X ), X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.87/1.28 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 0.87/1.28 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ =( 'c_Complex_OIm'( 'c_HOL_Ouminus__class_Ouminus'( X,
% 0.87/1.28 'tc_Complex_Ocomplex' ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.28 'c_Complex_OIm'( X ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.28 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.87/1.28 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.87/1.28 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.87/1.28 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.28 [ =( 'c_Complex_ORe'( 'c_Complex_Oii' ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ =( 'c_Transcendental_Osin'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( =( 'c_Complex_Ocomplex_OComplex'( X, Y ), 'c_Complex_Oii' ) ), =( X
% 0.87/1.28 , 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ =( 'c_NthRoot_Osqrt'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' )
% 0.87/1.28 ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oinverse__class_Oinverse'(
% 0.87/1.28 Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.28 Z, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), X ) ), =( Z,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.87/1.28 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_RealVector_Odist__class_Odist'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_RealVector_Odist__class_Odist'( Y, T, X ),
% 0.87/1.28 'c_RealVector_Odist__class_Odist'( T, Z, X ), 'tc_RealDef_Oreal' ),
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_RealVector_Odist__class_Odist'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_RealVector_Odist__class_Odist'( Y, T, X ),
% 0.87/1.28 'c_RealVector_Odist__class_Odist'( Z, T, X ), 'tc_RealDef_Oreal' ),
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_RealVector_Odist__class_Odist'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_RealVector_Odist__class_Odist'( T, Y, X ),
% 0.87/1.28 'c_RealVector_Odist__class_Odist'( T, Z, X ), 'tc_RealDef_Oreal' ),
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ =( 'c_Transcendental_Osin'( 'c_HOL_Ouminus__class_Ouminus'( X,
% 0.87/1.28 'tc_RealDef_Oreal' ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.28 'c_Transcendental_Osin'( X ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 0.87/1.28 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 0.87/1.28 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y
% 0.87/1.28 , X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.87/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Z
% 0.87/1.28 , X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ), =( Z,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 0.87/1.28 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ =( 'c_Transcendental_Ocos'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_RealVector_Ometric__space'( X ) ), =(
% 0.87/1.28 'c_RealVector_Odist__class_Odist'( Y, Z, X ),
% 0.87/1.28 'c_RealVector_Odist__class_Odist'( Z, Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 0.87/1.28 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 0.87/1.28 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 0.87/1.28 , X ) ) ],
% 0.87/1.28 [ ~( =( 'c_NthRoot_Osqrt'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' ) ), =( X,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), X ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 0.87/1.28 , X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 0.87/1.28 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ =( 'c_Complex_OIm'( 'c_Complex_Ocomplex_OComplex'( X, Y ) ), Y ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( =( 'c_Transcendental_Ocos'( X ), 'c_HOL_Oone__class_Oone'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ) ), =( 'c_Transcendental_Osin'( X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( =( 'c_NthRoot_Osqrt'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.28 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 Z, T, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.28 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.87/1.28 X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 0.87/1.28 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.28 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.28 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.28 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.28 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.28 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.28 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.28 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.87/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.28 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.87/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.87/1.28 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.28 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.28 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.28 ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.87/1.28 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.87/1.28 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.28 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.87/1.28 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.87/1.28 , X ), W, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.87/1.28 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 0.87/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 0.87/1.28 W, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.87/1.28 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.87/1.28 , X ), T, X ), W, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.87/1.28 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 0.87/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 0.87/1.28 W, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.28 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.87/1.28 , Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.87/1.28 X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.87/1.28 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.87/1.28 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.28 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 ) ), =( Y, Z ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 ) ), =( Y, Z ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.28 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.87/1.28 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.28 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.87/1.28 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.87/1.28 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.87/1.28 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.87/1.28 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.87/1.28 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.87/1.28 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.87/1.28 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ],
% 0.87/1.28 [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 0.87/1.28 'c_NthRoot_Osqrt'( X ), 'c_NthRoot_Osqrt'( Y ), 'tc_RealDef_Oreal' ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'c_lessequals'( 'c_NthRoot_Osqrt'( X ), 'c_NthRoot_Osqrt'( Y ),
% 0.87/1.28 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' )
% 0.87/1.28 , 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_RealDef_Oreal' ),
% 0.87/1.28 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Y, Z, 'tc_RealDef_Oreal' ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ =( 'c_NthRoot_Osqrt'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) )
% 0.87/1.28 , 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ) ],
% 0.87/1.28 [ ~( =( 'c_NthRoot_Osqrt'( X ), 'c_HOL_Oone__class_Oone'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.28 , X ), 'c_RealVector_Onorm__class_Onorm'( Y, X ) ) ],
% 0.87/1.28 [ =( 'c_Complex_Oii', 'c_Complex_Ocomplex_OComplex'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ) ],
% 0.87/1.28 [ =( 'c_Complex_Ocomplex_OComplex'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 'tc_RealDef_Oreal' ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ),
% 0.87/1.28 'c_Complex_Oii' ) ],
% 0.87/1.28 [ =( 'c_Complex_Ocomplex_OComplex'( 'c_HOL_Oone__class_Oone'(
% 0.87/1.28 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) )
% 0.87/1.28 , 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 0.87/1.28 [ =( 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'c_Complex_Ocomplex_OComplex'( 'c_HOL_Oone__class_Oone'(
% 0.87/1.28 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.28 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.28 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.28 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 0.87/1.28 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.28 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.87/1.28 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.87/1.28 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.28 Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X )
% 0.87/1.28 , 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.87/1.28 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ =( 'c_HOL_Ouminus__class_Ouminus'( 'c_Complex_Ocomplex_OComplex'( X, Y
% 0.87/1.28 ), 'tc_Complex_Ocomplex' ), 'c_Complex_Ocomplex_OComplex'(
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_RealDef_Oreal' ) ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.87/1.28 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.87/1.28 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 X ) ) ],
% 0.87/1.28 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Complex_Ocomplex_OComplex'( X, Y ),
% 0.87/1.28 'c_Complex_Ocomplex_OComplex'( Z, T ), 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'c_Complex_Ocomplex_OComplex'( 'c_HOL_Oplus__class_Oplus'( X, Z,
% 0.87/1.28 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.87/1.28 'tc_RealDef_Oreal' ) ) ) ],
% 0.87/1.28 [ =( 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'c_Complex_Ocomplex_OComplex'( 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.28 'c_Complex_ORe'( X ), 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_Complex_OIm'( X ), 'tc_RealDef_Oreal'
% 0.87/1.28 ) ) ) ],
% 0.87/1.28 [ =( 'c_NthRoot_Osqrt'( 'c_HOL_Ouminus__class_Ouminus'( X,
% 0.87/1.28 'tc_RealDef_Oreal' ) ), 'c_HOL_Ouminus__class_Ouminus'( 'c_NthRoot_Osqrt'(
% 0.87/1.28 X ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 0.87/1.28 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 0.87/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ), Z, X
% 0.87/1.28 ), 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 0.87/1.28 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.28 'c_lessequals'( Z, Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 0.87/1.28 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.28 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.87/1.28 'c_lessequals'( Z, Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 0.87/1.28 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 0.87/1.28 Y, Z, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__algebra__1'( X ) ), =(
% 0.87/1.28 'c_RealVector_Oof__real'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.87/1.28 'tc_RealDef_Oreal' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.28 'c_RealVector_Oof__real'( Y, X ), 'c_RealVector_Oof__real'( Z, X ), X ) )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 0.87/1.28 'class_RealVector_Oreal__algebra__1'( X ) ), =( 'c_RealVector_Oof__real'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_RealDef_Oreal' ), X ),
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( 'c_RealVector_Oof__real'( Y, X ),
% 0.87/1.28 'c_RealVector_Oof__real'( Z, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 0.87/1.28 [ =( 'c_Complex_ORe'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.28 'tc_Complex_Ocomplex' ) ), 'c_HOL_Ominus__class_Ominus'( 'c_Complex_ORe'(
% 0.87/1.28 X ), 'c_Complex_ORe'( Y ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ), =( Y,
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.28 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.87/1.28 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 0.87/1.28 , X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 0.87/1.28 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 0.87/1.28 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.87/1.28 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 0.87/1.28 Y, X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'(
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ),
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 0.87/1.28 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.28 , Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.87/1.28 , X ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.28 , Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 0.87/1.28 ],
% 0.87/1.28 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_RealDef_Oreal'
% 0.87/1.28 ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal'
% 0.87/1.28 ), ~( 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( =( 'c_Complex_OIm'( X ), 'c_Complex_OIm'( Y ) ) ), ~( =(
% 0.87/1.28 'c_Complex_ORe'( X ), 'c_Complex_ORe'( Y ) ) ), =( X, Y ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__algebra__1'( X ) ), =(
% 0.87/1.28 'c_RealVector_Oof__real'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.87/1.28 'tc_RealDef_Oreal' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_RealVector_Oof__real'( Y, X ), 'c_RealVector_Oof__real'( Z, X ), X ) )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 0.87/1.28 'class_RealVector_Oreal__algebra__1'( X ) ), =( 'c_RealVector_Oof__real'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_RealDef_Oreal' ), X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_RealVector_Oof__real'( Y, X ),
% 0.87/1.28 'c_RealVector_Oof__real'( Z, X ), X ) ) ],
% 0.87/1.28 [ =( 'c_Transcendental_Ocos'( 'c_HOL_Ouminus__class_Ouminus'( X,
% 0.87/1.28 'tc_RealDef_Oreal' ) ), 'c_Transcendental_Ocos'( X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.28 , X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 , X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ =( 'c_Complex_Ocomplex_OComplex'( 'c_Complex_ORe'( X ),
% 0.87/1.28 'c_Complex_OIm'( X ) ), X ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.87/1.28 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 0.87/1.28 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 0.87/1.28 Y, T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 0.87/1.28 ), Y, X ) ), =( Z, T ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 0.87/1.28 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.87/1.28 X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.87/1.28 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.87/1.28 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ =( 'c_Complex_ORe'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.28 'tc_Complex_Ocomplex' ) ), 'c_HOL_Oplus__class_Oplus'( 'c_Complex_ORe'( X
% 0.87/1.28 ), 'c_Complex_ORe'( Y ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.87/1.28 , Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.28 , Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.28 , T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.87/1.28 , T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.87/1.28 , Y, X ), X ) ) ],
% 0.87/1.28 [ =( 'c_Complex_ORe'( 'c_Complex_Ocomplex_OComplex'( X, Y ) ), X ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.87/1.28 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 0.87/1.28 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.28 Y, X ), X ) ],
% 0.87/1.28 [ =( 'c_Complex_OIm'( 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' )
% 0.87/1.28 ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.28 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.28 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.87/1.28 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.87/1.28 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.28 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X )
% 0.87/1.28 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 0.87/1.28 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 0.87/1.28 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.87/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.28 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 , X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y
% 0.87/1.28 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 0.87/1.28 X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X
% 0.87/1.28 ), X ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.87/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.87/1.28 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.87/1.28 , X ), W, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.87/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.87/1.28 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.87/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.28 Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.28 Z, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.87/1.28 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.28 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.87/1.28 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__algebra__1'( X ) ), =(
% 0.87/1.28 'c_RealVector_Oof__real'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' )
% 0.87/1.28 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_NthRoot_Osqrt'( X ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' ) )
% 0.87/1.28 ],
% 0.87/1.28 [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), X,
% 0.87/1.28 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 0.87/1.28 'tc_RealDef_Oreal' ), 'c_NthRoot_Osqrt'( X ), 'tc_RealDef_Oreal' ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_NthRoot_Osqrt'( X ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' ) )
% 0.87/1.28 ],
% 0.87/1.28 [ 'c_lessequals'( X, 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 0.87/1.28 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( 'c_NthRoot_Osqrt'( X ),
% 0.87/1.28 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'c_lessequals'( 'c_NthRoot_Osqrt'( X ), 'c_HOL_Oone__class_Oone'(
% 0.87/1.28 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( X,
% 0.87/1.28 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'c_lessequals'( 'c_Transcendental_Osin'( X ), 'c_HOL_Oone__class_Oone'(
% 0.87/1.28 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_Transcendental_Ocos'( X ), 'c_HOL_Oone__class_Oone'(
% 0.87/1.28 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Odist__norm'( X ) ), =(
% 0.87/1.28 'c_RealVector_Odist__class_Odist'( Y, Z, X ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 0.87/1.28 ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( Y, X ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'(
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( X, 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'( X,
% 0.87/1.28 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_Complex_ORe'( X ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( X, 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ ~( =( 'c_Complex_Ocomplex_OComplex'( X, Y ), 'c_Complex_Oii' ) ), =( Y
% 0.87/1.28 , 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ =( 'c_Complex_OIm'( 'c_Complex_Oii' ), 'c_HOL_Oone__class_Oone'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ =( 'c_Complex_ORe'( 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' )
% 0.87/1.28 ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( =( 'c_Complex_Ocomplex_OComplex'( X, Y ), 'c_HOL_Oone__class_Oone'(
% 0.87/1.28 'tc_Complex_Ocomplex' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ =( 'c_RealVector_Odist__class_Odist'( X, Y, 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.28 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ) ) ],
% 0.87/1.28 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.87/1.28 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y
% 0.87/1.28 , Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X
% 0.87/1.28 ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, U,
% 0.87/1.28 X ), X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.87/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.87/1.28 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.87/1.28 , X ), W, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 0.87/1.28 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.87/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.87/1.28 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.87/1.28 , X ), T, X ), W, X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.87/1.28 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X )
% 0.87/1.28 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_RealVector_Onorm__class_Onorm'( Y,
% 0.87/1.28 X ), 'c_RealVector_Onorm__class_Onorm'( Z, X ), 'tc_RealDef_Oreal' ),
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( Z, X ), 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X )
% 0.87/1.28 , X ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( Z, X ), 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 0.87/1.28 ), X ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 0.87/1.28 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_RealVector_Onorm__class_Onorm'( Y
% 0.87/1.28 , X ), 'c_RealVector_Onorm__class_Onorm'( Z, X ), 'tc_RealDef_Oreal' ),
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_RealVector_Onorm__class_Onorm'( X,
% 0.87/1.28 'tc_Complex_Ocomplex' ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.28 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( Y, 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 0.87/1.28 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( X, 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'( Y,
% 0.87/1.28 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_lessequals'(
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, U,
% 0.87/1.28 X ), X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( Y, T, X
% 0.87/1.28 ), X ), 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.28 Z, U, X ), X ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), 'c_lessequals'( Y, X,
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.87/1.28 'c_lessequals'( Z, Y, X ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.28 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.28 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 0.87/1.28 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 0.87/1.28 [ 'c_lessequals'( X, X, 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Z, Y,
% 0.87/1.28 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( X, Z, 'tc_RealDef_Oreal' ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ =( 'c_RealVector_Onorm__class_Onorm'( 'v_z', 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.87/1.28 X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.87/1.28 X ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.87/1.28 X ) ) ],
% 0.87/1.28 [ ~( =( 'c_Complex_Oii', 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 0.87/1.28 ) ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 0.87/1.28 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.28 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ), =(
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.87/1.28 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.87/1.28 X ) ) ), =( Y, T ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.87/1.28 X ) ) ), =( Z, T ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.87/1.28 X ) ) ), =( Z, T ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.28 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.87/1.28 X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.87/1.28 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.87/1.28 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.28 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.28 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.87/1.28 X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.28 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.87/1.28 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.87/1.28 X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.87/1.28 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.87/1.28 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.87/1.28 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.28 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_RealDef_Oreal' ) ), ~(
% 0.87/1.28 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.87/1.28 ), Y ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.28 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.87/1.28 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.28 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.28 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.87/1.28 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.28 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.87/1.28 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.87/1.28 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.87/1.28 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.87/1.28 , T, X ) ) ), =( Z, T ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.87/1.28 , T, X ) ) ), =( Y, Z ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.87/1.28 , U, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 0.87/1.28 ), X ), 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.28 Z, Y, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.87/1.28 ), Y ) ],
% 0.87/1.28 [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( 'v_z',
% 0.87/1.28 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 0.87/1.28 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 0.87/1.28 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_Complex_Oii', 'tc_Complex_Ocomplex'
% 0.87/1.28 ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( 'v_z',
% 0.87/1.28 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 0.87/1.28 ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z',
% 0.87/1.28 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 0.87/1.28 ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z',
% 0.87/1.28 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 0.87/1.28 ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( 'v_z',
% 0.87/1.28 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 0.87/1.28 ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z',
% 0.87/1.28 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( 'v_z',
% 0.87/1.28 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.87/1.28 ],
% 0.87/1.28 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.87/1.28 ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.87/1.28 ],
% 0.87/1.28 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_RealDef_Oreal'
% 0.87/1.28 ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 0.87/1.28 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_RealDef_Oreal'
% 0.87/1.28 ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_RealDef_Oreal'
% 0.87/1.28 ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_RealDef_Oreal' )
% 0.87/1.28 ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_RealDef_Oreal' )
% 0.87/1.28 ],
% 0.87/1.28 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_RealDef_Oreal' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_RealVector_Oreal__normed__vector'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oordered__field'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_RealVector_Oreal__algebra__1'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Oab__group__add'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Omult__zero'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Omult__mono'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Osemiring'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_RealVector_Ometric__space'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oring__1'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oabs__if'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Ofield'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_RealVector_Odist__norm'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oring'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Power_Opower'( 'tc_RealDef_Oreal' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 0.87/1.28 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 0.87/1.28 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 0.87/1.28 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 0.87/1.28 ],
% 0.87/1.28 [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_Complex_Ocomplex' )
% 0.87/1.28 ],
% 0.87/1.28 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 0.87/1.28 ],
% 0.87/1.28 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 0.87/1.28 ],
% 0.87/1.28 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_RealVector_Oreal__normed__vector'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_RealVector_Oreal__algebra__1'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_RealVector_Ometric__space'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_RealVector_Odist__norm'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 0.87/1.28 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ]
% 0.87/1.28 ] .
% 0.87/1.28
% 0.87/1.28
% 0.87/1.28 percentage equality = 0.210801, percentage horn = 0.922853
% 0.87/1.28 This is a problem with some equality
% 0.87/1.28
% 0.87/1.28
% 0.87/1.28
% 0.87/1.28 Options Used:
% 0.87/1.28
% 0.87/1.28 useres = 1
% 0.87/1.28 useparamod = 1
% 0.87/1.28 useeqrefl = 1
% 0.87/1.28 useeqfact = 1
% 0.87/1.28 usefactor = 1
% 0.87/1.28 usesimpsplitting = 0
% 0.87/1.28 usesimpdemod = 5
% 0.87/1.28 usesimpres = 3
% 0.87/1.28
% 0.87/1.28 resimpinuse = 1000
% 0.87/1.28 resimpclauses = 20000
% 0.87/1.28 substype = eqrewr
% 0.87/1.28 backwardsubs = 1
% 0.87/1.28 selectoldest = 5
% 0.87/1.28
% 0.87/1.28 litorderings [0] = split
% 0.87/1.28 litorderings [1] = extend the termordering, first sorting on arguments
% 0.87/1.28
% 0.87/1.28 termordering = kbo
% 0.87/1.28
% 0.87/1.28 litapriori = 0
% 0.87/1.28 termapriori = 1
% 0.87/1.28 litaposteriori = 0
% 0.87/1.28 termaposteriori = 0
% 0.87/1.28 demodaposteriori = 0
% 0.87/1.28 ordereqreflfact = 0
% 0.87/1.28
% 0.87/1.28 litselect = negord
% 0.87/1.28
% 0.87/1.28 maxweight = 15
% 0.87/1.28 maxdepth = 30000
% 0.87/1.28 maxlength = 115
% 0.87/1.28 maxnrvars = 195
% 0.87/1.28 excuselevel = 1
% 0.87/1.28 increasemaxweight = 1
% 0.87/1.28
% 0.87/1.28 maxselected = 10000000
% 0.87/1.28 maxnrclauses = 10000000
% 0.87/1.28
% 0.87/1.28 showgenerated = 0
% 0.87/1.28 showkept = 0
% 0.87/1.28 showselected = 0
% 0.87/1.28 showdeleted = 0
% 0.87/1.28 showresimp = 1
% 0.87/1.28 showstatus = 2000
% 0.87/1.28
% 0.87/1.28 prologoutput = 1
% 0.87/1.28 nrgoals = 5000000
% 0.87/1.28 totalproof = 1
% 0.87/1.28
% 0.87/1.28 Symbols occurring in the translation:
% 0.87/1.28
% 0.87/1.28 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.87/1.28 . [1, 2] (w:1, o:120, a:1, s:1, b:0),
% 0.87/1.28 ! [4, 1] (w:0, o:47, a:1, s:1, b:0),
% 0.87/1.28 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.87/1.28 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.87/1.28 'class_Ring__and__Field_Ocomm__semiring__1' [40, 1] (w:1, o:52, a:1
% 0.87/1.28 , s:1, b:0),
% 0.87/1.28 'c_HOL_Otimes__class_Otimes' [43, 3] (w:1, o:151, a:1, s:1, b:0),
% 0.87/1.28 'class_Orderings_Oorder' [44, 1] (w:1, o:53, a:1, s:1, b:0),
% 0.87/1.28 'c_HOL_Oord__class_Oless' [47, 3] (w:1, o:152, a:1, s:1, b:0),
% 0.87/1.28 'class_Orderings_Opreorder' [49, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.87/1.28 'c_Complex_Ocomplex_OComplex' [50, 2] (w:1, o:145, a:1, s:1, b:0),
% 0.87/1.28 'tc_Complex_Ocomplex' [51, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.87/1.28 'c_HOL_Oone__class_Oone' [52, 1] (w:1, o:55, a:1, s:1, b:0),
% 0.87/1.28 'tc_RealDef_Oreal' [53, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero' [54, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.87/1.28 'class_OrderedGroup_Opordered__ab__group__add__abs' [55, 1] (w:1, o:
% 0.87/1.28 58, a:1, s:1, b:0),
% 0.87/1.28 'c_HOL_Oabs__class_Oabs' [56, 2] (w:1, o:146, a:1, s:1, b:0),
% 0.87/1.28 'class_OrderedGroup_Ogroup__add' [57, 1] (w:1, o:59, a:1, s:1, b:0),
% 0.87/1.28
% 0.87/1.28 'c_HOL_Ouminus__class_Ouminus' [58, 2] (w:1, o:147, a:1, s:1, b:0),
% 0.87/1.28 'c_Complex_ORe' [59, 1] (w:1, o:60, a:1, s:1, b:0),
% 0.87/1.28 'class_Ring__and__Field_Oordered__semidom' [60, 1] (w:1, o:66, a:1
% 0.87/1.28 , s:1, b:0),
% 0.87/1.28 'c_Power_Opower__class_Opower' [62, 3] (w:1, o:153, a:1, s:1, b:0),
% 0.87/1.28 'c_lessequals' [63, 3] (w:1, o:154, a:1, s:1, b:0),
% 0.87/1.28 'class_Ring__and__Field_Oordered__idom' [64, 1] (w:1, o:67, a:1, s:1
% 0.87/1.28 , b:0),
% 0.87/1.28 'class_Ring__and__Field_Oordered__semiring__strict' [65, 1] (w:1, o:
% 0.87/1.28 68, a:1, s:1, b:0),
% 0.87/1.28 'class_Ring__and__Field_Oordered__ring__strict' [67, 1] (w:1, o:65
% 0.87/1.28 , a:1, s:1, b:0),
% 0.87/1.28 'class_Ring__and__Field_Oordered__field' [68, 1] (w:1, o:69, a:1, s:1
% 0.87/1.28 , b:0),
% 0.87/1.28 'class_Ring__and__Field_Odivision__by__zero' [69, 1] (w:1, o:71, a:1
% 0.87/1.28 , s:1, b:0),
% 0.87/1.28 'c_HOL_Oinverse__class_Oinverse' [70, 2] (w:1, o:148, a:1, s:1, b:0)
% 0.87/1.28 ,
% 0.87/1.28 'c_HOL_Oplus__class_Oplus' [71, 3] (w:1, o:155, a:1, s:1, b:0),
% 0.87/1.28 'class_OrderedGroup_Oab__group__add' [72, 1] (w:1, o:72, a:1, s:1, b:
% 0.87/1.28 0),
% 0.87/1.28 'class_Ring__and__Field_Odivision__ring' [73, 1] (w:1, o:73, a:1, s:1
% 0.87/1.28 , b:0),
% 0.87/1.28 'class_OrderedGroup_Opordered__ab__group__add' [75, 1] (w:1, o:74, a:
% 0.87/1.28 1, s:1, b:0),
% 0.87/1.28 'class_Ring__and__Field_Olordered__ring' [76, 1] (w:1, o:75, a:1, s:1
% 0.87/1.28 , b:0),
% 0.87/1.28 'class_RealVector_Oreal__algebra__1' [77, 1] (w:1, o:76, a:1, s:1, b:
% 0.87/1.28 0),
% 0.87/1.28 'c_RealVector_Oof__real' [78, 2] (w:1, o:150, a:1, s:1, b:0),
% 0.87/1.28 'class_RealVector_Oreal__normed__vector' [79, 1] (w:1, o:77, a:1, s:1
% 0.87/1.28 , b:0),
% 0.87/1.28 'c_RealVector_Onorm__class_Onorm' [80, 2] (w:1, o:149, a:1, s:1, b:0)
% 0.87/1.28 ,
% 0.87/1.28 'c_HOL_Ominus__class_Ominus' [81, 3] (w:1, o:156, a:1, s:1, b:0),
% 0.87/1.28 'c_Complex_OIm' [82, 1] (w:1, o:78, a:1, s:1, b:0),
% 0.87/1.28 'class_Ring__and__Field_Oordered__semiring' [83, 1] (w:1, o:79, a:1
% 0.87/1.28 , s:1, b:0),
% 0.87/1.28 'class_Ring__and__Field_Oidom' [84, 1] (w:1, o:80, a:1, s:1, b:0),
% 0.87/1.28 'class_Orderings_Olinorder' [85, 1] (w:1, o:81, a:1, s:1, b:0),
% 2.31/2.67 'class_OrderedGroup_Olordered__ab__group__add__abs' [86, 1] (w:1, o:
% 2.31/2.67 82, a:1, s:1, b:0),
% 2.31/2.67 'class_Ring__and__Field_Oabs__if' [87, 1] (w:1, o:83, a:1, s:1, b:0)
% 2.31/2.67 ,
% 2.31/2.67 'class_Ring__and__Field_Ono__zero__divisors' [88, 1] (w:1, o:64, a:1
% 2.31/2.67 , s:1, b:0),
% 2.31/2.67 'class_Ring__and__Field_Oring__no__zero__divisors' [89, 1] (w:1, o:84
% 2.31/2.67 , a:1, s:1, b:0),
% 2.31/2.67 'class_OrderedGroup_Olordered__ab__group__add' [90, 1] (w:1, o:85, a:
% 2.31/2.67 1, s:1, b:0),
% 2.31/2.67 'class_RealVector_Ometric__space' [91, 1] (w:1, o:86, a:1, s:1, b:0)
% 2.31/2.67 ,
% 2.31/2.67 'c_RealVector_Odist__class_Odist' [92, 3] (w:1, o:157, a:1, s:1, b:0)
% 2.31/2.67 ,
% 2.31/2.67 'class_Lattices_Oboolean__algebra' [97, 1] (w:1, o:87, a:1, s:1, b:0)
% 2.31/2.67 ,
% 2.31/2.67 'class_Ring__and__Field_Opordered__ring__abs' [98, 1] (w:1, o:89, a:1
% 2.31/2.67 , s:1, b:0),
% 2.31/2.67 'class_Ring__and__Field_Oring' [99, 1] (w:1, o:90, a:1, s:1, b:0),
% 2.31/2.67 'class_OrderedGroup_Oab__semigroup__idem__mult' [100, 1] (w:1, o:91
% 2.31/2.67 , a:1, s:1, b:0),
% 2.31/2.67 'class_Ring__and__Field_Ozero__neq__one' [101, 1] (w:1, o:92, a:1, s:
% 2.31/2.67 1, b:0),
% 2.31/2.67 'class_Ring__and__Field_Omult__zero' [102, 1] (w:1, o:61, a:1, s:1
% 2.31/2.67 , b:0),
% 2.31/2.67 'class_Power_Opower' [103, 1] (w:1, o:105, a:1, s:1, b:0),
% 2.31/2.67 'class_Ring__and__Field_Oring__1__no__zero__divisors' [104, 1] (w:1
% 2.31/2.67 , o:106, a:1, s:1, b:0),
% 2.31/2.67 'c_NthRoot_Osqrt' [105, 1] (w:1, o:107, a:1, s:1, b:0),
% 2.31/2.67 'class_Ring__and__Field_Omult__mono1' [110, 1] (w:1, o:62, a:1, s:1
% 2.31/2.67 , b:0),
% 2.31/2.67 'class_Ring__and__Field_Omult__mono' [111, 1] (w:1, o:63, a:1, s:1
% 2.31/2.67 , b:0),
% 2.31/2.67 'class_Ring__and__Field_Opordered__ring' [112, 1] (w:1, o:108, a:1
% 2.31/2.67 , s:1, b:0),
% 2.31/2.67 'class_Int_Onumber__ring' [113, 1] (w:1, o:109, a:1, s:1, b:0),
% 2.31/2.67 'class_OrderedGroup_Opordered__comm__monoid__add' [115, 1] (w:1, o:93
% 2.31/2.67 , a:1, s:1, b:0),
% 2.31/2.67 'c_Transcendental_Ocos' [116, 1] (w:1, o:110, a:1, s:1, b:0),
% 2.31/2.67 'c_Transcendental_Osin' [117, 1] (w:1, o:111, a:1, s:1, b:0),
% 2.31/2.67 'class_Ring__and__Field_Oordered__comm__semiring__strict' [118, 1]
% 2.31/2.67 (w:1, o:88, a:1, s:1, b:0),
% 2.31/2.67 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [120, 1]
% 2.31/2.67 (w:1, o:94, a:1, s:1, b:0),
% 2.31/2.67 'class_OrderedGroup_Ocomm__monoid__add' [121, 1] (w:1, o:95, a:1, s:1
% 2.31/2.67 , b:0),
% 2.31/2.67 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [122, 1]
% 2.31/2.67 (w:1, o:96, a:1, s:1, b:0),
% 2.31/2.67 'class_OrderedGroup_Ocomm__monoid__mult' [124, 1] (w:1, o:97, a:1, s:
% 2.31/2.67 1, b:0),
% 2.31/2.67 'class_Ring__and__Field_Opordered__cancel__semiring' [125, 1] (w:1
% 2.31/2.67 , o:112, a:1, s:1, b:0),
% 2.31/2.67 'class_OrderedGroup_Oab__semigroup__mult' [126, 1] (w:1, o:98, a:1
% 2.31/2.67 , s:1, b:0),
% 2.31/2.67 'class_OrderedGroup_Oordered__ab__group__add' [127, 1] (w:1, o:57, a:
% 2.31/2.67 1, s:1, b:0),
% 2.31/2.67 'class_RealVector_Oreal__normed__algebra' [128, 1] (w:1, o:113, a:1
% 2.31/2.67 , s:1, b:0),
% 2.31/2.67 'class_Ring__and__Field_Ofield' [130, 1] (w:1, o:114, a:1, s:1, b:0)
% 2.31/2.67 ,
% 2.31/2.67 'class_Ring__and__Field_Opordered__semiring' [131, 1] (w:1, o:115, a:
% 2.31/2.67 1, s:1, b:0),
% 2.31/2.67 'c_Complex_Oii' [132, 0] (w:1, o:40, a:1, s:1, b:0),
% 2.31/2.67 'class_Ring__and__Field_Ocomm__semiring' [135, 1] (w:1, o:70, a:1, s:
% 2.31/2.67 1, b:0),
% 2.31/2.67 'class_Ring__and__Field_Osemiring' [139, 1] (w:1, o:117, a:1, s:1, b:
% 2.31/2.67 0),
% 2.31/2.67 'class_OrderedGroup_Omonoid__add' [141, 1] (w:1, o:99, a:1, s:1, b:0)
% 2.31/2.67 ,
% 2.31/2.67 'class_OrderedGroup_Omonoid__mult' [142, 1] (w:1, o:100, a:1, s:1, b:
% 2.31/2.67 0),
% 2.31/2.67 'class_Ring__and__Field_Oring__1' [145, 1] (w:1, o:116, a:1, s:1, b:0
% 2.31/2.67 ),
% 2.31/2.67 'class_RealVector_Odist__norm' [146, 1] (w:1, o:118, a:1, s:1, b:0),
% 2.31/2.67
% 2.31/2.67 'v_z' [150, 0] (w:1, o:44, a:1, s:1, b:0),
% 2.31/2.67 'class_OrderedGroup_Opordered__ab__semigroup__add' [151, 1] (w:1, o:
% 2.31/2.67 101, a:1, s:1, b:0),
% 2.31/2.67 'class_RealVector_Oreal__normed__algebra__1' [153, 1] (w:1, o:119, a:
% 2.31/2.67 1, s:1, b:0),
% 2.31/2.67 'class_OrderedGroup_Ocancel__semigroup__add' [154, 1] (w:1, o:102, a:
% 2.31/2.67 1, s:1, b:0),
% 2.31/2.67 'class_OrderedGroup_Ocancel__ab__semigroup__add' [155, 1] (w:1, o:103
% 2.31/2.67 , a:1, s:1, b:0),
% 2.31/2.67 'class_OrderedGroup_Oab__semigroup__add' [156, 1] (w:1, o:104, a:1
% 2.31/2.67 , s:1, b:0),
% 2.31/2.67 'tc_nat' [157, 0] (w:1, o:46, a:1, s:1, b:0).
% 2.31/2.67
% 2.31/2.67
% 2.31/2.67 Starting Search:
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67
% 2.31/2.67 Intermediate Status:
% 2.31/2.67 Generated: 3228
% 2.31/2.67 Kept: 2006
% 2.31/2.67 Inuse: 151
% 2.31/2.67 Deleted: 2
% 2.31/2.67 Deletedinuse: 0
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67
% 2.31/2.67 Intermediate Status:
% 2.31/2.67 Generated: 10929
% 2.31/2.67 Kept: 4501
% 2.31/2.67 Inuse: 199
% 2.31/2.67 Deleted: 2
% 2.31/2.67 Deletedinuse: 0
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67
% 2.31/2.67 Intermediate Status:
% 2.31/2.67 Generated: 18480
% 2.31/2.67 Kept: 6510
% 2.31/2.67 Inuse: 286
% 2.31/2.67 Deleted: 4
% 2.31/2.67 Deletedinuse: 0
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67
% 2.31/2.67 Intermediate Status:
% 2.31/2.67 Generated: 28948
% 2.31/2.67 Kept: 8731
% 2.31/2.67 Inuse: 333
% 2.31/2.67 Deleted: 8
% 2.31/2.67 Deletedinuse: 0
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67
% 2.31/2.67 Intermediate Status:
% 2.31/2.67 Generated: 39101
% 2.31/2.67 Kept: 10776
% 2.31/2.67 Inuse: 393
% 2.31/2.67 Deleted: 8
% 2.31/2.67 Deletedinuse: 0
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67
% 2.31/2.67 Intermediate Status:
% 2.31/2.67 Generated: 47956
% 2.31/2.67 Kept: 12875
% 2.31/2.67 Inuse: 438
% 2.31/2.67 Deleted: 8
% 2.31/2.67 Deletedinuse: 0
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67
% 2.31/2.67 Intermediate Status:
% 2.31/2.67 Generated: 61143
% 2.31/2.67 Kept: 16027
% 2.31/2.67 Inuse: 483
% 2.31/2.67 Deleted: 8
% 2.31/2.67 Deletedinuse: 0
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67
% 2.31/2.67 Intermediate Status:
% 2.31/2.67 Generated: 68576
% 2.31/2.67 Kept: 18031
% 2.31/2.67 Inuse: 500
% 2.31/2.67 Deleted: 8
% 2.31/2.67 Deletedinuse: 0
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67 Resimplifying inuse:
% 2.31/2.67 Done
% 2.31/2.67
% 2.31/2.67 Resimplifying clauses:
% 2.31/2.67
% 2.31/2.67 Bliksems!, er is een bewijs:
% 2.31/2.67 % SZS status Unsatisfiable
% 2.31/2.67 % SZS output start Refutation
% 2.31/2.67
% 2.31/2.67 clause( 488, [ =( 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.67 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_Complex_Ocomplex' ),
% 2.31/2.67 'tc_Complex_Ocomplex' ), 'c_RealVector_Odist__class_Odist'( X, Y,
% 2.31/2.67 'tc_Complex_Ocomplex' ) ) ] )
% 2.31/2.67 .
% 2.31/2.67 clause( 544, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.67 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.67 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_Complex_Oii', 'tc_Complex_Ocomplex'
% 2.31/2.67 ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.67 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z',
% 2.31/2.67 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 2.31/2.67 ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.67 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_Complex_Oii',
% 2.31/2.67 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.67 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.67 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) )
% 2.31/2.67 ] )
% 2.31/2.67 .
% 2.31/2.67 clause( 545, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal'
% 2.31/2.67 ), 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z'
% 2.31/2.67 , 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ),
% 2.31/2.67 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ]
% 2.31/2.67 )
% 2.31/2.67 .
% 2.31/2.67 clause( 546, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal'
% 2.31/2.67 ), 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.67 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ]
% 2.31/2.67 )
% 2.31/2.67 .
% 2.31/2.67 clause( 547, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal'
% 2.31/2.67 ), 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z'
% 2.31/2.67 , 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 2.31/2.67 'tc_RealDef_Oreal' ) ] )
% 2.31/2.67 .
% 2.31/2.67 clause( 548, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal'
% 2.31/2.67 ), 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_Complex_Oii',
% 2.31/2.67 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ] )
% 2.31/2.67 .
% 2.31/2.67 clause( 20027, [] )
% 2.31/2.67 .
% 2.31/2.67
% 2.31/2.67
% 2.31/2.67 % SZS output end Refutation
% 2.31/2.67 found a proof!
% 2.31/2.67
% 2.31/2.67 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.31/2.67
% 2.31/2.67 initialclauses(
% 2.31/2.67 [ clause( 20029, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.67 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.67 Z, Y, X ) ) ] )
% 2.31/2.67 , clause( 20030, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 2.31/2.67 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 2.31/2.67 , clause( 20031, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 2.31/2.67 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.31/2.67 , clause( 20032, [ ~( =( 'c_Complex_Ocomplex_OComplex'( X, Y ),
% 2.31/2.67 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ), =( Y,
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.67 , clause( 20033, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.67 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.31/2.67 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.67 , clause( 20034, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 2.31/2.67 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ] )
% 2.31/2.67 , clause( 20035, [ =( 'c_Complex_ORe'( 'c_HOL_Ouminus__class_Ouminus'( X,
% 2.31/2.67 'tc_Complex_Ocomplex' ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 2.31/2.67 'c_Complex_ORe'( X ), 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.67 , clause( 20036, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.67 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.31/2.67 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 2.31/2.67 ] )
% 2.31/2.67 , clause( 20037, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20038, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y
% 2.31/2.67 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.31/2.67 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 2.31/2.67 ), X ) ) ] )
% 2.31/2.67 , clause( 20039, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.67 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 2.31/2.67 , T, X ), X ) ) ] )
% 2.31/2.67 , clause( 20040, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.67 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.31/2.67 , Z, X ), X ) ) ] )
% 2.31/2.67 , clause( 20041, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.67 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 2.31/2.67 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 2.31/2.67 ) ) ] )
% 2.31/2.67 , clause( 20042, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.67 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.31/2.67 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.67 X ), T, X ) ) ] )
% 2.31/2.67 , clause( 20043, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.67 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 2.31/2.67 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 2.31/2.67 ) ) ] )
% 2.31/2.67 , clause( 20044, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.67 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.31/2.67 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20045, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.31/2.67 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 2.31/2.67 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.31/2.67 , clause( 20046, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.67 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 2.31/2.67 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.67 , clause( 20047, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.31/2.67 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 2.31/2.67 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.67 , clause( 20048, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.67 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.67 Z, Y, X ) ) ] )
% 2.31/2.67 , clause( 20049, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.31/2.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.31/2.67 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 2.31/2.67 ), X ), Y ) ] )
% 2.31/2.67 , clause( 20050, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.67 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 2.31/2.67 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 2.31/2.67 ] )
% 2.31/2.67 , clause( 20051, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.67 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20052, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.67 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.67 , clause( 20053, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.67 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.67 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.67 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.31/2.67 , clause( 20054, [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ),
% 2.31/2.67 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y
% 2.31/2.67 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y
% 2.31/2.67 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ] )
% 2.31/2.67 , clause( 20055, [ ~( 'class_RealVector_Oreal__algebra__1'( X ) ), ~( =(
% 2.31/2.67 'c_RealVector_Oof__real'( Y, X ), 'c_RealVector_Oof__real'( Z, X ) ) ),
% 2.31/2.67 =( Y, Z ) ] )
% 2.31/2.67 , clause( 20056, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.67 X ) ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'(
% 2.31/2.67 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 2.31/2.67 ) ] )
% 2.31/2.67 , clause( 20057, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 2.31/2.67 =( 'c_RealVector_Onorm__class_Onorm'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.67 'tc_RealDef_Oreal' ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.67 , clause( 20058, [ =( 'c_Complex_OIm'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.31/2.67 'tc_Complex_Ocomplex' ) ), 'c_HOL_Ominus__class_Ominus'( 'c_Complex_OIm'(
% 2.31/2.67 X ), 'c_Complex_OIm'( Y ), 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.67 , clause( 20059, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.31/2.67 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_RealDef_Oreal' ),
% 2.31/2.67 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) )
% 2.31/2.67 ), =( X, Y ) ] )
% 2.31/2.67 , clause( 20060, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.31/2.67 , Z, X ), X ) ) ] )
% 2.31/2.67 , clause( 20061, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 2.31/2.67 , T, X ), X ) ) ] )
% 2.31/2.67 , clause( 20062, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.67 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.31/2.67 , Z, X ), X ) ) ] )
% 2.31/2.67 , clause( 20063, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.67 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 2.31/2.67 , T, X ), X ) ) ] )
% 2.31/2.67 , clause( 20064, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 2.31/2.67 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 2.31/2.67 )
% 2.31/2.67 , clause( 20065, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.31/2.67 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 2.31/2.67 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 2.31/2.67 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.31/2.67 ) ] )
% 2.31/2.67 , clause( 20066, [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 2.31/2.67 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 2.31/2.67 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.31/2.67 ) ] )
% 2.31/2.67 , clause( 20067, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.67 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.31/2.67 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 2.31/2.67 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20068, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 2.31/2.67 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.67 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.67 , clause( 20069, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 2.31/2.67 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.67 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.67 , clause( 20070, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 2.31/2.67 ) ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 2.31/2.67 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.67 , clause( 20071, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20072, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20073, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.67 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20074, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.67 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20075, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.67 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20076, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.67 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.67 , clause( 20077, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.67 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.31/2.67 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 2.31/2.67 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 2.31/2.67 , clause( 20078, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.67 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.31/2.67 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 2.31/2.67 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.31/2.67 , clause( 20079, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.67 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 2.31/2.67 Z, T, X ), X ) ) ] )
% 2.31/2.67 , clause( 20080, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 2.31/2.67 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 2.31/2.67 ) ] )
% 2.31/2.67 , clause( 20081, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.67 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 2.31/2.67 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20082, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.31/2.67 'tc_Complex_Ocomplex' ), 'c_Complex_Ocomplex_OComplex'(
% 2.31/2.67 'c_HOL_Oplus__class_Oplus'( 'c_Complex_ORe'( X ), 'c_Complex_ORe'( Y ),
% 2.31/2.67 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( 'c_Complex_OIm'( X ),
% 2.31/2.67 'c_Complex_OIm'( Y ), 'tc_RealDef_Oreal' ) ) ) ] )
% 2.31/2.67 , clause( 20083, [ ~( 'class_RealVector_Ometric__space'( X ) ), =(
% 2.31/2.67 'c_RealVector_Odist__class_Odist'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.67 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.67 , clause( 20084, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.67 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.67 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 2.31/2.67 , X ), X ) ) ] )
% 2.31/2.67 , clause( 20085, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.67 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.31/2.67 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.67 Z, Y, X ) ) ] )
% 2.31/2.67 , clause( 20086, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 2.31/2.67 'class_RealVector_Oreal__algebra__1'( X ) ), =( 'c_RealVector_Oof__real'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.67 , clause( 20087, [ ~( 'class_RealVector_Oreal__algebra__1'( X ) ), =(
% 2.31/2.67 'c_RealVector_Oof__real'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal'
% 2.31/2.67 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.67 , clause( 20088, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.31/2.67 'c_Complex_Ocomplex_OComplex'( X, Y ), 'c_Complex_Ocomplex_OComplex'( Z,
% 2.31/2.67 T ), 'tc_Complex_Ocomplex' ), 'c_Complex_Ocomplex_OComplex'(
% 2.31/2.67 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_RealDef_Oreal' ),
% 2.31/2.67 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_RealDef_Oreal' ) ) ) ] )
% 2.31/2.67 , clause( 20089, [ ~( 'class_RealVector_Ometric__space'( X ) ),
% 2.31/2.67 'c_lessequals'( 'c_RealVector_Odist__class_Odist'( Y, Y, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ]
% 2.31/2.67 )
% 2.31/2.67 , clause( 20090, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.31/2.67 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 2.31/2.67 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.67 , clause( 20091, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.67 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.67 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 2.31/2.67 , clause( 20092, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.67 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.67 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 2.31/2.67 , clause( 20093, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.67 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.67 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 2.31/2.67 , clause( 20094, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.67 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20095, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.67 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 2.31/2.67 ] )
% 2.31/2.67 , clause( 20096, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.31/2.67 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 2.31/2.67 , X ) ) ), =( Y, Z ) ] )
% 2.31/2.67 , clause( 20097, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 2.31/2.67 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 2.31/2.67 , X ) ) ), =( Y, Z ) ] )
% 2.31/2.67 , clause( 20098, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 2.31/2.67 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 2.31/2.67 , Y, X ) ) ] )
% 2.31/2.67 , clause( 20099, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 2.31/2.67 ), =( Z, Y ) ] )
% 2.31/2.67 , clause( 20100, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 2.31/2.67 , clause( 20101, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 2.31/2.67 ) ] )
% 2.31/2.67 , clause( 20102, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 2.31/2.67 ) ] )
% 2.31/2.67 , clause( 20103, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 2.31/2.67 ), =( Z, Y ) ] )
% 2.31/2.67 , clause( 20104, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.67 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.67 , clause( 20105, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.31/2.67 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 2.31/2.67 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.31/2.67 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 2.31/2.67 , clause( 20106, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 2.31/2.67 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 2.31/2.67 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.31/2.67 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.67 , clause( 20107, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 2.31/2.67 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 2.31/2.67 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.31/2.67 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.67 , clause( 20108, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 2.31/2.67 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 2.31/2.67 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.31/2.67 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20109, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 2.31/2.67 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 2.31/2.67 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.31/2.67 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20110, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.31/2.67 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.67 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 2.31/2.67 , Z, X ) ) ] )
% 2.31/2.67 , clause( 20111, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.31/2.67 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.67 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 2.31/2.67 X ), X ) ) ] )
% 2.31/2.67 , clause( 20112, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.31/2.67 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 2.31/2.67 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Y,
% 2.31/2.67 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ),
% 2.31/2.67 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.67 , clause( 20113, [ 'c_lessequals'( X, 'c_HOL_Ouminus__class_Ouminus'( Y,
% 2.31/2.67 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_RealDef_Oreal' ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 2.31/2.67 ] )
% 2.31/2.67 , clause( 20114, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 2.31/2.67 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y,
% 2.31/2.67 Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 2.31/2.67 , clause( 20115, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.67 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.31/2.67 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.31/2.67 , clause( 20116, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 2.31/2.67 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 2.31/2.67 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 2.31/2.67 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 2.31/2.67 ) ) ] )
% 2.31/2.67 , clause( 20117, [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 2.31/2.67 X ) ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 2.31/2.67 ) ) ] )
% 2.31/2.67 , clause( 20118, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.67 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.31/2.67 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20119, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.67 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.67 , clause( 20120, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 2.31/2.67 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 2.31/2.67 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.31/2.67 , clause( 20121, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.67 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.67 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.31/2.67 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20122, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.67 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.31/2.67 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.31/2.67 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 2.31/2.67 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.67 , clause( 20123, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.67 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.67 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.31/2.67 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20124, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.31/2.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20125, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.68 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.68 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20126, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.68 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.68 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20127, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.68 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.68 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20128, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 2.31/2.68 ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20129, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_NthRoot_Osqrt'( X ), 'tc_RealDef_Oreal' ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), X,
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20130, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'c_NthRoot_Osqrt'( X )
% 2.31/2.68 , 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20131, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_NthRoot_Osqrt'( X ), 'tc_RealDef_Oreal' ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), X,
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20132, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.31/2.68 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20133, [ ~( =( 'c_NthRoot_Osqrt'( X ), 'c_NthRoot_Osqrt'( Y ) ) )
% 2.31/2.68 , =( X, Y ) ] )
% 2.31/2.68 , clause( 20134, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 2.31/2.68 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20135, [ ~( =( 'c_Complex_Ocomplex_OComplex'( X, Y ),
% 2.31/2.68 'c_Complex_Ocomplex_OComplex'( Z, T ) ) ), =( Y, T ) ] )
% 2.31/2.68 , clause( 20136, [ ~( =( 'c_Complex_Ocomplex_OComplex'( X, Y ),
% 2.31/2.68 'c_Complex_Ocomplex_OComplex'( Z, T ) ) ), =( X, Z ) ] )
% 2.31/2.68 , clause( 20137, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 2.31/2.68 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 2.31/2.68 , Y, X ) ) ] )
% 2.31/2.68 , clause( 20138, [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20139, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20140, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20141, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20142, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20143, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.31/2.68 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20144, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 2.31/2.68 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20145, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 2.31/2.68 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20146, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.31/2.68 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 2.31/2.68 ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ] )
% 2.31/2.68 , clause( 20147, [ ~( 'class_RealVector_Ometric__space'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 2.31/2.68 'c_RealVector_Odist__class_Odist'( Y, Z, X ), 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20148, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.31/2.68 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20149, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 2.31/2.68 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20150, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ),
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20151, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.31/2.68 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20152, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20153, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20154, [ 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 2.31/2.68 'c_NthRoot_Osqrt'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' )
% 2.31/2.68 , 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20155, [ 'c_lessequals'( 'c_NthRoot_Osqrt'( X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ),
% 2.31/2.68 ~( 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20156, [ ~( 'class_RealVector_Ometric__space'( X ) ), ~( =(
% 2.31/2.68 'c_RealVector_Odist__class_Odist'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ), =( Y, Z ) ] )
% 2.31/2.68 , clause( 20157, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 2.31/2.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20158, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 2.31/2.68 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20159, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 2.31/2.68 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20160, [ =( 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.68 'c_Complex_Ocomplex_OComplex'( 'c_Transcendental_Ocos'( X ),
% 2.31/2.68 'c_Transcendental_Osin'( X ) ), 'tc_Complex_Ocomplex' ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20161, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20162, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20163, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20164, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20165, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20166, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20167, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20168, [ ~( 'class_RealVector_Ometric__space'( X ) ), =( Y, Z ),
% 2.31/2.68 ~( 'c_lessequals'( 'c_RealVector_Odist__class_Odist'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20169, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20170, [ ~(
% 2.31/2.68 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.31/2.68 , clause( 20171, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20172, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20173, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.68 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.68 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.31/2.68 , clause( 20174, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 2.31/2.68 , clause( 20175, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20176, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20177, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.68 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.68 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.31/2.68 , clause( 20178, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 2.31/2.68 , clause( 20179, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20180, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.31/2.68 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 X ), T, X ) ) ] )
% 2.31/2.68 , clause( 20181, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20182, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.31/2.68 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20183, [ 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( X,
% 2.31/2.68 'tc_RealDef_Oreal' ), Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_RealDef_Oreal' ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20184, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.31/2.68 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ), Y,
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20185, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20186, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.31/2.68 ), Y ) ] )
% 2.31/2.68 , clause( 20187, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20188, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20189, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.31/2.68 ), Y ) ] )
% 2.31/2.68 , clause( 20190, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.31/2.68 ), Y ) ] )
% 2.31/2.68 , clause( 20191, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X
% 2.31/2.68 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X )
% 2.31/2.68 , Y, X ) ) ] )
% 2.31/2.68 , clause( 20192, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X
% 2.31/2.68 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X )
% 2.31/2.68 , Y, X ) ) ] )
% 2.31/2.68 , clause( 20193, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X
% 2.31/2.68 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 2.31/2.68 ), X ) ) ] )
% 2.31/2.68 , clause( 20194, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X
% 2.31/2.68 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 2.31/2.68 ), X ) ) ] )
% 2.31/2.68 , clause( 20195, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 2.31/2.68 , clause( 20196, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 2.31/2.68 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 2.31/2.68 , clause( 20197, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.31/2.68 , clause( 20198, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 2.31/2.68 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.31/2.68 , clause( 20199, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 2.31/2.68 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.31/2.68 , clause( 20200, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 2.31/2.68 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.31/2.68 , clause( 20201, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 2.31/2.68 'c_lessequals'( Y, Z, X ) ) ] )
% 2.31/2.68 , clause( 20202, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 2.31/2.68 , clause( 20203, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20204, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 2.31/2.68 Z, Y ) ] )
% 2.31/2.68 , clause( 20205, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.31/2.68 , clause( 20206, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 2.31/2.68 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 2.31/2.68 , clause( 20207, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 2.31/2.68 Y, Z ) ] )
% 2.31/2.68 , clause( 20208, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20209, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.31/2.68 , clause( 20210, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20211, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 2.31/2.68 , X ), X ) ) ] )
% 2.31/2.68 , clause( 20212, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20213, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20214, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'(
% 2.31/2.68 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 2.31/2.68 , clause( 20215, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 2.31/2.68 , clause( 20216, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 2.31/2.68 Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.31/2.68 , clause( 20217, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 2.31/2.68 , clause( 20218, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20219, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.31/2.68 , Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 2.31/2.68 , clause( 20220, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 2.31/2.68 , clause( 20221, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 2.31/2.68 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 2.31/2.68 , clause( 20222, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20223, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20224, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 2.31/2.68 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20225, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 2.31/2.68 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20226, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 2.31/2.68 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X
% 2.31/2.68 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20227, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.31/2.68 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20228, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.31/2.68 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20229, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20230, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20231, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), X
% 2.31/2.68 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 2.31/2.68 , clause( 20232, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.31/2.68 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20233, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.31/2.68 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20234, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ] )
% 2.31/2.68 , clause( 20235, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 2.31/2.68 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20236, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 X ), X ) ) ] )
% 2.31/2.68 , clause( 20237, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 X ), X ) ) ] )
% 2.31/2.68 , clause( 20238, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~(
% 2.31/2.68 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20239, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~(
% 2.31/2.68 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20240, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 2.31/2.68 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20241, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 2.31/2.68 X ) ) ] )
% 2.31/2.68 , clause( 20242, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 2.31/2.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20243, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 2.31/2.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20244, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 Y, T, X ) ) ] )
% 2.31/2.68 , clause( 20245, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 Y, T, X ) ) ] )
% 2.31/2.68 , clause( 20246, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 2.31/2.68 X ), X ) ) ] )
% 2.31/2.68 , clause( 20247, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 Z, T, X ) ) ] )
% 2.31/2.68 , clause( 20248, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 2.31/2.68 ), =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 2.31/2.68 , clause( 20249, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.68 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.68 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.31/2.68 , clause( 20250, [ ~( 'class_RealVector_Oreal__algebra__1'( X ) ), ~( =(
% 2.31/2.68 'c_RealVector_Oof__real'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 2.31/2.68 =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20251, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ] )
% 2.31/2.68 , clause( 20252, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.31/2.68 =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20253, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20254, [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.31/2.68 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20255, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 2.31/2.68 ), T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 2.31/2.68 Y, T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20256, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 2.31/2.68 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 2.31/2.68 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20257, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 2.31/2.68 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 2.31/2.68 Y, X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20258, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 2.31/2.68 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 2.31/2.68 Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20259, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20260, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20261, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20262, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ] )
% 2.31/2.68 , clause( 20263, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20264, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20265, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20266, [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ), Y, X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20267, [ =( 'c_Complex_OIm'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.31/2.68 'tc_Complex_Ocomplex' ) ), 'c_HOL_Oplus__class_Oplus'( 'c_Complex_OIm'( X
% 2.31/2.68 ), 'c_Complex_OIm'( Y ), 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20268, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 2.31/2.68 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 2.31/2.68 T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20269, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.68 , T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y,
% 2.31/2.68 T, X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20270, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.68 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 Z, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20271, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 2.31/2.68 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 2.31/2.68 , X ), T, X ) ) ] )
% 2.31/2.68 , clause( 20272, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 2.31/2.68 ), X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y
% 2.31/2.68 , T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20273, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 2.31/2.68 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 2.31/2.68 , X ), T, X ) ) ] )
% 2.31/2.68 , clause( 20274, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20275, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20276, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20277, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20278, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20279, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20280, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20281, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 2.31/2.68 , ~( =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20282, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ] )
% 2.31/2.68 , clause( 20283, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 2.31/2.68 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 2.31/2.68 X ), X ) ) ] )
% 2.31/2.68 , clause( 20284, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 2.31/2.68 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 2.31/2.68 X ), X ) ) ] )
% 2.31/2.68 , clause( 20285, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 2.31/2.68 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 2.31/2.68 X ), X ) ) ] )
% 2.31/2.68 , clause( 20286, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 2.31/2.68 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 2.31/2.68 X ), X ) ) ] )
% 2.31/2.68 , clause( 20287, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 Y, Y, X ) ) ] )
% 2.31/2.68 , clause( 20288, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 Y, Z, X ) ) ] )
% 2.31/2.68 , clause( 20289, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 2.31/2.68 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 X ) ) ] )
% 2.31/2.68 , clause( 20290, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 2.31/2.68 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 X ) ) ] )
% 2.31/2.68 , clause( 20291, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 2.31/2.68 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 X ) ) ] )
% 2.31/2.68 , clause( 20292, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 2.31/2.68 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.31/2.68 , clause( 20293, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 2.31/2.68 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.31/2.68 , clause( 20294, [ ~( 'class_RealVector_Oreal__algebra__1'( X ) ), =(
% 2.31/2.68 'c_RealVector_Oof__real'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 2.31/2.68 'tc_RealDef_Oreal' ), X ), 'c_HOL_Ouminus__class_Ouminus'(
% 2.31/2.68 'c_RealVector_Oof__real'( Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20295, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 2.31/2.68 'class_RealVector_Oreal__algebra__1'( X ) ), =( 'c_RealVector_Oof__real'(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_RealDef_Oreal' ), X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_RealVector_Oof__real'( Y, X ), X ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20296, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 2.31/2.68 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 2.31/2.68 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20297, [ =( 'c_Complex_OIm'( 'c_HOL_Ouminus__class_Ouminus'( X,
% 2.31/2.68 'tc_Complex_Ocomplex' ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 2.31/2.68 'c_Complex_OIm'( X ), 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20298, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20299, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 2.31/2.68 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 2.31/2.68 X ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20300, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20301, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 2.31/2.68 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 2.31/2.68 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20302, [ =( 'c_Complex_ORe'( 'c_Complex_Oii' ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20303, [ =( 'c_Transcendental_Osin'( 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20304, [ ~( =( 'c_Complex_Ocomplex_OComplex'( X, Y ),
% 2.31/2.68 'c_Complex_Oii' ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal'
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20305, [ =( 'c_NthRoot_Osqrt'( 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20306, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20307, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oinverse__class_Oinverse'(
% 2.31/2.68 Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20308, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 2.31/2.68 Z, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20309, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ] )
% 2.31/2.68 , clause( 20310, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), X ) ), =( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20311, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( X,
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_RealDef_Oreal' ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20312, [ ~( 'class_RealVector_Ometric__space'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_RealVector_Odist__class_Odist'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_RealVector_Odist__class_Odist'( Y, T, X )
% 2.31/2.68 , 'c_RealVector_Odist__class_Odist'( T, Z, X ), 'tc_RealDef_Oreal' ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20313, [ ~( 'class_RealVector_Ometric__space'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_RealVector_Odist__class_Odist'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_RealVector_Odist__class_Odist'( Y, T, X )
% 2.31/2.68 , 'c_RealVector_Odist__class_Odist'( Z, T, X ), 'tc_RealDef_Oreal' ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20314, [ ~( 'class_RealVector_Ometric__space'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_RealVector_Odist__class_Odist'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_RealVector_Odist__class_Odist'( T, Y, X )
% 2.31/2.68 , 'c_RealVector_Odist__class_Odist'( T, Z, X ), 'tc_RealDef_Oreal' ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20315, [ =( 'c_Transcendental_Osin'(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ) ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_Transcendental_Osin'( X ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20316, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 2.31/2.68 'c_lessequals'( Y, Z, X ) ) ] )
% 2.31/2.68 , clause( 20317, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 2.31/2.68 'c_lessequals'( Y, Z, X ) ) ] )
% 2.31/2.68 , clause( 20318, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 2.31/2.68 ), X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 2.31/2.68 , clause( 20319, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 2.31/2.68 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20320, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20321, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20322, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20323, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20324, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20325, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20326, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20327, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.68 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y
% 2.31/2.68 , X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20328, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.68 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Z
% 2.31/2.68 , X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ), =( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20329, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20330, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 2.31/2.68 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20331, [ =( 'c_Transcendental_Ocos'( 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20332, [ ~( 'class_RealVector_Ometric__space'( X ) ), =(
% 2.31/2.68 'c_RealVector_Odist__class_Odist'( Y, Z, X ),
% 2.31/2.68 'c_RealVector_Odist__class_Odist'( Z, Y, X ) ) ] )
% 2.31/2.68 , clause( 20333, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20334, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20335, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 2.31/2.68 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20336, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 2.31/2.68 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20337, [ ~( =( 'c_NthRoot_Osqrt'( X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' ) ), =( X,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20338, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20339, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 2.31/2.68 , clause( 20340, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20341, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 2.31/2.68 , clause( 20342, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 2.31/2.68 , X ) ] )
% 2.31/2.68 , clause( 20343, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20344, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 2.31/2.68 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20345, [ =( 'c_Complex_OIm'( 'c_Complex_Ocomplex_OComplex'( X, Y
% 2.31/2.68 ) ), Y ) ] )
% 2.31/2.68 , clause( 20346, [ ~( =( 'c_Transcendental_Ocos'( X ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ), =(
% 2.31/2.68 'c_Transcendental_Osin'( X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20347, [ ~( =( 'c_NthRoot_Osqrt'( X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20348, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 Z, T, X ) ) ] )
% 2.31/2.68 , clause( 20349, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 2.31/2.68 X ), X ) ) ] )
% 2.31/2.68 , clause( 20350, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 2.31/2.68 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20351, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ] )
% 2.31/2.68 , clause( 20352, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ] )
% 2.31/2.68 , clause( 20353, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.31/2.68 , clause( 20354, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.31/2.68 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.31/2.68 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 2.31/2.68 =( Y, T ) ] )
% 2.31/2.68 , clause( 20355, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.31/2.68 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.31/2.68 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 2.31/2.68 =( Y, T ) ] )
% 2.31/2.68 , clause( 20356, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20357, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 2.31/2.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20358, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 2.31/2.68 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 2.31/2.68 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20359, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 2.31/2.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20360, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 2.31/2.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20361, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 2.31/2.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20362, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 2.31/2.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20363, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 2.31/2.68 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X
% 2.31/2.68 ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20364, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ] )
% 2.31/2.68 , clause( 20365, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.68 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20366, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.31/2.68 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 2.31/2.68 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20367, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.31/2.68 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.31/2.68 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20368, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.31/2.68 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.31/2.68 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20369, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.68 , =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20370, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 2.31/2.68 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 2.31/2.68 , clause( 20371, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.31/2.68 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ] )
% 2.31/2.68 , clause( 20372, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20373, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20374, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20375, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.31/2.68 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20376, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20377, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20378, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20379, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20380, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 2.31/2.68 , clause( 20381, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.31/2.68 , clause( 20382, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.31/2.68 , clause( 20383, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 2.31/2.68 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.31/2.68 , clause( 20384, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 2.31/2.68 =( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20385, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.31/2.68 , clause( 20386, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 2.31/2.68 =( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20387, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20388, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20389, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20390, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20391, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20392, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20393, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 2.31/2.68 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.31/2.68 , clause( 20394, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.31/2.68 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ] )
% 2.31/2.68 , clause( 20395, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 2.31/2.68 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 2.31/2.68 , X ), W, X ), X ) ) ] )
% 2.31/2.68 , clause( 20396, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 2.31/2.68 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 2.31/2.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 2.31/2.68 W, X ), X ) ) ] )
% 2.31/2.68 , clause( 20397, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 2.31/2.68 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 2.31/2.68 , X ), T, X ), W, X ) ) ] )
% 2.31/2.68 , clause( 20398, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 2.31/2.68 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 2.31/2.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 2.31/2.68 W, X ), X ) ) ] )
% 2.31/2.68 , clause( 20399, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.31/2.68 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 2.31/2.68 , Y, X ) ) ] )
% 2.31/2.68 , clause( 20400, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.31/2.68 X ) ) ] )
% 2.31/2.68 , clause( 20401, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 2.31/2.68 ), X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X
% 2.31/2.68 ), X ) ) ] )
% 2.31/2.68 , clause( 20402, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 2.31/2.68 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.31/2.68 , clause( 20403, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 2.31/2.68 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 2.31/2.68 , clause( 20404, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20405, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20406, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20407, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20408, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.31/2.68 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 2.31/2.68 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20409, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 ) ), =( Y, Z ) ] )
% 2.31/2.68 , clause( 20410, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 ) ), =( Y, Z ) ] )
% 2.31/2.68 , clause( 20411, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.31/2.68 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 2.31/2.68 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 2.31/2.68 , clause( 20412, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 2.31/2.68 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 2.31/2.68 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20413, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 2.31/2.68 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 2.31/2.68 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20414, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 2.31/2.68 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 2.31/2.68 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20415, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 2.31/2.68 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 2.31/2.68 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20416, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.31/2.68 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ] )
% 2.31/2.68 , clause( 20417, [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~(
% 2.31/2.68 'c_lessequals'( 'c_NthRoot_Osqrt'( X ), 'c_NthRoot_Osqrt'( Y ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20418, [ 'c_lessequals'( 'c_NthRoot_Osqrt'( X ),
% 2.31/2.68 'c_NthRoot_Osqrt'( Y ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( X, Y,
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20419, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_HOL_Oplus__class_Oplus'( X, Z,
% 2.31/2.68 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Y, Z,
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20420, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20421, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =( Y
% 2.31/2.68 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20422, [ =( 'c_NthRoot_Osqrt'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20423, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ) ] )
% 2.31/2.68 , clause( 20424, [ ~( =( 'c_NthRoot_Osqrt'( X ), 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20425, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 2.31/2.68 , X ), 'c_RealVector_Onorm__class_Onorm'( Y, X ) ) ] )
% 2.31/2.68 , clause( 20426, [ =( 'c_Complex_Oii', 'c_Complex_Ocomplex_OComplex'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ) ] )
% 2.31/2.68 , clause( 20427, [ =( 'c_Complex_Ocomplex_OComplex'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ), 'c_Complex_Oii' ) ] )
% 2.31/2.68 , clause( 20428, [ =( 'c_Complex_Ocomplex_OComplex'(
% 2.31/2.68 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ] )
% 2.31/2.68 , clause( 20429, [ =( 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ),
% 2.31/2.68 'c_Complex_Ocomplex_OComplex'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20430, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.31/2.68 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20431, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20432, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20433, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20434, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20435, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.31/2.68 ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20436, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20437, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.31/2.68 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20438, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.31/2.68 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20439, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 2.31/2.68 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 2.31/2.68 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 2.31/2.68 , clause( 20440, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 2.31/2.68 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 2.31/2.68 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20441, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.31/2.68 ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20442, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 2.31/2.68 X ) ] )
% 2.31/2.68 , clause( 20443, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 2.31/2.68 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.31/2.68 , clause( 20444, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.31/2.68 , clause( 20445, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.68 ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20446, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 X ) ) ] )
% 2.31/2.68 , clause( 20447, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 X ), X ) ] )
% 2.31/2.68 , clause( 20448, [ =( 'c_HOL_Ouminus__class_Ouminus'(
% 2.31/2.68 'c_Complex_Ocomplex_OComplex'( X, Y ), 'tc_Complex_Ocomplex' ),
% 2.31/2.68 'c_Complex_Ocomplex_OComplex'( 'c_HOL_Ouminus__class_Ouminus'( X,
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_HOL_Ouminus__class_Ouminus'( Y,
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ) ] )
% 2.31/2.68 , clause( 20449, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20450, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20451, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.31/2.68 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20452, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 2.31/2.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20453, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20454, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20455, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.31/2.68 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20456, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 2.31/2.68 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20457, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20458, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20459, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X )
% 2.31/2.68 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 2.31/2.68 , clause( 20460, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 X ) ) ] )
% 2.31/2.68 , clause( 20461, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_Complex_Ocomplex_OComplex'( X, Y ), 'c_Complex_Ocomplex_OComplex'( Z,
% 2.31/2.68 T ), 'tc_Complex_Ocomplex' ), 'c_Complex_Ocomplex_OComplex'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_RealDef_Oreal' ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, T, 'tc_RealDef_Oreal' ) ) ) ] )
% 2.31/2.68 , clause( 20462, [ =( 'c_HOL_Ouminus__class_Ouminus'( X,
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'c_Complex_Ocomplex_OComplex'(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_Complex_ORe'( X ), 'tc_RealDef_Oreal'
% 2.31/2.68 ), 'c_HOL_Ouminus__class_Ouminus'( 'c_Complex_OIm'( X ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ) ] )
% 2.31/2.68 , clause( 20463, [ =( 'c_NthRoot_Osqrt'( 'c_HOL_Ouminus__class_Ouminus'( X
% 2.31/2.68 , 'tc_RealDef_Oreal' ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 2.31/2.68 'c_NthRoot_Osqrt'( X ), 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20464, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20465, [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 2.31/2.68 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 2.31/2.68 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ), Z, X
% 2.31/2.68 ), 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20466, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.31/2.68 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20467, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.31/2.68 'c_lessequals'( Z, Y, X ) ) ] )
% 2.31/2.68 , clause( 20468, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.31/2.68 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20469, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.31/2.68 'c_lessequals'( Z, Y, X ) ) ] )
% 2.31/2.68 , clause( 20470, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.31/2.68 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 2.31/2.68 Y, Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20471, [ ~( 'class_RealVector_Oreal__algebra__1'( X ) ), =(
% 2.31/2.68 'c_RealVector_Oof__real'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 2.31/2.68 'tc_RealDef_Oreal' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 2.31/2.68 'c_RealVector_Oof__real'( Y, X ), 'c_RealVector_Oof__real'( Z, X ), X ) )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20472, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 2.31/2.68 'class_RealVector_Oreal__algebra__1'( X ) ), =( 'c_RealVector_Oof__real'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_RealDef_Oreal' ), X ),
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'c_RealVector_Oof__real'( Y, X ),
% 2.31/2.68 'c_RealVector_Oof__real'( Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20473, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 2.31/2.68 , clause( 20474, [ =( 'c_Complex_ORe'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.31/2.68 'tc_Complex_Ocomplex' ) ), 'c_HOL_Ominus__class_Ominus'( 'c_Complex_ORe'(
% 2.31/2.68 X ), 'c_Complex_ORe'( Y ), 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20475, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20476, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ) )
% 2.31/2.68 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20477, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 2.31/2.68 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ] )
% 2.31/2.68 , clause( 20478, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 2.31/2.68 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ] )
% 2.31/2.68 , clause( 20479, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.68 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20480, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20481, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20482, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 2.31/2.68 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 2.31/2.68 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20483, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 2.31/2.68 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 2.31/2.68 Y, X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20484, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.31/2.68 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20485, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.31/2.68 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20486, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20487, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20488, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20489, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20490, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.31/2.68 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20491, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20492, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20493, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 2.31/2.68 ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 2.31/2.68 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20494, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 2.31/2.68 ) ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20495, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ),
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20496, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 2.31/2.68 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20497, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.31/2.68 , clause( 20498, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.31/2.68 , clause( 20499, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.31/2.68 , clause( 20500, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.31/2.68 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20501, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20502, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20503, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20504, [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_RealDef_Oreal' )
% 2.31/2.68 , 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20505, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 2.31/2.68 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20506, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20507, [ ~( =( 'c_Complex_OIm'( X ), 'c_Complex_OIm'( Y ) ) ),
% 2.31/2.68 ~( =( 'c_Complex_ORe'( X ), 'c_Complex_ORe'( Y ) ) ), =( X, Y ) ] )
% 2.31/2.68 , clause( 20508, [ ~( 'class_RealVector_Oreal__algebra__1'( X ) ), =(
% 2.31/2.68 'c_RealVector_Oof__real'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 2.31/2.68 'tc_RealDef_Oreal' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_RealVector_Oof__real'( Y, X ), 'c_RealVector_Oof__real'( Z, X ), X ) )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20509, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 2.31/2.68 'class_RealVector_Oreal__algebra__1'( X ) ), =( 'c_RealVector_Oof__real'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_RealDef_Oreal' ), X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_RealVector_Oof__real'( Y, X ),
% 2.31/2.68 'c_RealVector_Oof__real'( Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20510, [ =( 'c_Transcendental_Ocos'(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( X, 'tc_RealDef_Oreal' ) ),
% 2.31/2.68 'c_Transcendental_Ocos'( X ) ) ] )
% 2.31/2.68 , clause( 20511, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20512, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20513, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20514, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ), X ) ] )
% 2.31/2.68 , clause( 20515, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20516, [ =( 'c_Complex_Ocomplex_OComplex'( 'c_Complex_ORe'( X ),
% 2.31/2.68 'c_Complex_OIm'( X ) ), X ) ] )
% 2.31/2.68 , clause( 20517, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20518, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.31/2.68 =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20519, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.68 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.68 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.31/2.68 , clause( 20520, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.68 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.31/2.68 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.31/2.68 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20521, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.68 ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.31/2.68 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 2.31/2.68 , T ) ] )
% 2.31/2.68 , clause( 20522, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 2.31/2.68 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 2.31/2.68 X ), X ) ) ] )
% 2.31/2.68 , clause( 20523, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20524, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 2.31/2.68 , =( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.31/2.68 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20525, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.31/2.68 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 2.31/2.68 , clause( 20526, [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 2.31/2.68 , clause( 20527, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), ~( =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.31/2.68 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.31/2.68 , clause( 20528, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20529, [ =( 'c_Complex_ORe'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.31/2.68 'tc_Complex_Ocomplex' ) ), 'c_HOL_Oplus__class_Oplus'( 'c_Complex_ORe'( X
% 2.31/2.68 ), 'c_Complex_ORe'( Y ), 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20530, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20531, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 2.31/2.68 , Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20532, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20533, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.31/2.68 , Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20534, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.31/2.68 , T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20535, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.31/2.68 , T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20536, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.31/2.68 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.31/2.68 , Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20537, [ =( 'c_Complex_ORe'( 'c_Complex_Ocomplex_OComplex'( X, Y
% 2.31/2.68 ) ), X ) ] )
% 2.31/2.68 , clause( 20538, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20539, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.31/2.68 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.31/2.68 , clause( 20540, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20541, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 2.31/2.68 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20542, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 2.31/2.68 , clause( 20543, [ =( 'c_Complex_OIm'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_Complex_Ocomplex' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal'
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20544, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.31/2.68 Y, X ) ) ] )
% 2.31/2.68 , clause( 20545, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.31/2.68 Y, X ) ) ] )
% 2.31/2.68 , clause( 20546, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.31/2.68 Y, X ) ) ] )
% 2.31/2.68 , clause( 20547, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.31/2.68 Y, X ) ) ] )
% 2.31/2.68 , clause( 20548, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.31/2.68 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 2.31/2.68 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20549, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 2.31/2.68 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20550, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 2.31/2.68 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20551, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 2.31/2.68 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ] )
% 2.31/2.68 , clause( 20552, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 2.31/2.68 , clause( 20553, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.31/2.68 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 2.31/2.68 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 2.31/2.68 , clause( 20554, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20555, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.31/2.68 , clause( 20556, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20557, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ] )
% 2.31/2.68 , clause( 20558, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 2.31/2.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 2.31/2.68 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 2.31/2.68 , X ), W, X ) ) ] )
% 2.31/2.68 , clause( 20559, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 2.31/2.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 2.31/2.68 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 2.31/2.68 , clause( 20560, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 2.31/2.68 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20561, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20562, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20563, [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20564, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20565, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20566, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 2.31/2.68 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 2.31/2.68 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ] )
% 2.31/2.68 , clause( 20567, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 2.31/2.68 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ] )
% 2.31/2.68 , clause( 20568, [ ~( 'class_RealVector_Oreal__algebra__1'( X ) ), =(
% 2.31/2.68 'c_RealVector_Oof__real'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' )
% 2.31/2.68 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.31/2.68 , clause( 20569, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_NthRoot_Osqrt'( X ), 'tc_RealDef_Oreal' ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), X,
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20570, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ), X, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'c_NthRoot_Osqrt'( X ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20571, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_NthRoot_Osqrt'( X ), 'tc_RealDef_Oreal' ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), X,
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20572, [ 'c_lessequals'( X, 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~( 'c_lessequals'(
% 2.31/2.68 'c_NthRoot_Osqrt'( X ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20573, [ 'c_lessequals'( 'c_NthRoot_Osqrt'( X ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ), ~(
% 2.31/2.68 'c_lessequals'( X, 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20574, [ 'c_lessequals'( 'c_Transcendental_Osin'( X ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20575, [ 'c_lessequals'( 'c_Transcendental_Ocos'( X ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20576, [ ~( 'class_RealVector_Odist__norm'( X ) ), =(
% 2.31/2.68 'c_RealVector_Odist__class_Odist'( Y, Z, X ),
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 2.31/2.68 ), X ) ) ] )
% 2.31/2.68 , clause( 20577, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_RealDef_Oreal' ),
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( Y, X ), 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20578, [ 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'(
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( X, 'tc_Complex_Ocomplex' ),
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'( X,
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20579, [ 'c_lessequals'( 'c_Complex_ORe'( X ),
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( X, 'tc_Complex_Ocomplex' ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20580, [ ~( =( 'c_Complex_Ocomplex_OComplex'( X, Y ),
% 2.31/2.68 'c_Complex_Oii' ) ), =( Y, 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20581, [ =( 'c_Complex_OIm'( 'c_Complex_Oii' ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20582, [ =( 'c_Complex_ORe'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_Complex_Ocomplex' ) ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20583, [ ~( =( 'c_Complex_Ocomplex_OComplex'( X, Y ),
% 2.31/2.68 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ), =( X,
% 2.31/2.68 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20584, [ =( 'c_RealVector_Odist__class_Odist'( X, Y,
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_Complex_Ocomplex' ),
% 2.31/2.68 'tc_Complex_Ocomplex' ) ) ] )
% 2.31/2.68 , clause( 20585, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'c_HOL_Oplus__class_Oplus'( X,
% 2.31/2.68 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_Complex_Ocomplex' ),
% 2.31/2.68 'tc_Complex_Ocomplex' ) ) ] )
% 2.31/2.68 , clause( 20586, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 2.31/2.68 X ) ] )
% 2.31/2.68 , clause( 20587, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ] )
% 2.31/2.68 , clause( 20588, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 T, 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z, X ), W, X ), X ) ) ] )
% 2.31/2.68 , clause( 20589, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.31/2.68 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 2.31/2.68 , X ), W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X
% 2.31/2.68 ), X ) ) ] )
% 2.31/2.68 , clause( 20590, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W, X ) ) ] )
% 2.31/2.68 , clause( 20591, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 2.31/2.68 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.31/2.68 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ] )
% 2.31/2.68 , clause( 20592, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( Z, X ), 'tc_RealDef_Oreal' ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20593, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( Z, X ), 'tc_RealDef_Oreal' ),
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X )
% 2.31/2.68 , X ), 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20594, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( Z, X ), 'tc_RealDef_Oreal' ),
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 2.31/2.68 ), X ), 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20595, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( Y, X ),
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( Z, X ), 'tc_RealDef_Oreal' ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20596, [ 'c_lessequals'( 'c_RealVector_Onorm__class_Onorm'( X,
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( Y, 'tc_Complex_Ocomplex' ),
% 2.31/2.68 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20597, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( X, 'tc_Complex_Ocomplex' ),
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'( Y,
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20598, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ),
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( Z, U, X
% 2.31/2.68 ), X ), 'tc_RealDef_Oreal' ), 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20599, [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ),
% 2.31/2.68 'c_lessequals'( Y, X, 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20600, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.31/2.68 , Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 2.31/2.68 , clause( 20601, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 2.31/2.68 , X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20602, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 2.31/2.68 , Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20603, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 2.31/2.68 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ] )
% 2.31/2.68 , clause( 20604, [ 'c_lessequals'( X, X, 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20605, [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~(
% 2.31/2.68 'c_lessequals'( Z, Y, 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( X, Z,
% 2.31/2.68 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20606, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y
% 2.31/2.68 , X ) ] )
% 2.31/2.68 , clause( 20607, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 2.31/2.68 , Y, X ) ] )
% 2.31/2.68 , clause( 20608, [ =( 'c_RealVector_Onorm__class_Onorm'( 'v_z',
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20609, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 2.31/2.68 X ) ) ] )
% 2.31/2.68 , clause( 20610, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 2.31/2.68 Y, X ) ) ] )
% 2.31/2.68 , clause( 20611, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 2.31/2.68 Y, X ) ) ] )
% 2.31/2.68 , clause( 20612, [ ~( =( 'c_Complex_Oii', 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_Complex_Ocomplex' ) ) ) ] )
% 2.31/2.68 , clause( 20613, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 2.31/2.68 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 2.31/2.68 ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.31/2.68 , clause( 20614, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.31/2.68 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 2.31/2.68 , clause( 20615, [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ),
% 2.31/2.68 =( 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oone__class_Oone'( X ), X )
% 2.31/2.68 , 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20616, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 2.31/2.68 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 T, Z, X ) ) ), =( Y, T ) ] )
% 2.31/2.68 , clause( 20617, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 2.31/2.68 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 Y, T, X ) ) ), =( Z, T ) ] )
% 2.31/2.68 , clause( 20618, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 2.31/2.68 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 2.31/2.68 , clause( 20619, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.31/2.68 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 2.31/2.68 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 2.31/2.68 , clause( 20620, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 2.31/2.68 X ), X ) ) ] )
% 2.31/2.68 , clause( 20621, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 2.31/2.68 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 2.31/2.68 , clause( 20622, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.31/2.68 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 2.31/2.68 ~( 'c_lessequals'( U, T, X ) ) ] )
% 2.31/2.68 , clause( 20623, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20624, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.31/2.68 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 2.31/2.68 , clause( 20625, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.31/2.68 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20626, [ ~(
% 2.31/2.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.31/2.68 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ) ) ] )
% 2.31/2.68 , clause( 20627, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 2.31/2.68 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20628, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 2.31/2.68 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20629, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 2.31/2.68 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 2.31/2.68 , clause( 20630, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 2.31/2.68 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.31/2.68 , clause( 20631, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 2.31/2.68 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.31/2.68 , clause( 20632, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_RealDef_Oreal' )
% 2.31/2.68 ), ~( 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20633, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 2.31/2.68 ), Y ) ] )
% 2.31/2.68 , clause( 20634, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.31/2.68 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20635, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 2.31/2.68 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20636, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 2.31/2.68 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20637, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.31/2.68 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20638, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 2.31/2.68 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 20639, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 2.31/2.68 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20640, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 2.31/2.68 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20641, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 2.31/2.68 X ), 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X )
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20642, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.31/2.68 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 2.31/2.68 X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , clause( 20643, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 2.31/2.68 , T, X ) ) ), =( Z, T ) ] )
% 2.31/2.68 , clause( 20644, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 2.31/2.68 , T, X ) ) ), =( Y, Z ) ] )
% 2.31/2.68 , clause( 20645, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 2.31/2.68 , U, X ), X ) ) ] )
% 2.31/2.68 , clause( 20646, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 2.31/2.68 ), X ), 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ominus__class_Ominus'(
% 2.31/2.68 Z, Y, X ), X ) ) ] )
% 2.31/2.68 , clause( 20647, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 2.31/2.68 ), Y ) ] )
% 2.31/2.68 , clause( 20648, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'v_z', 'c_Complex_Oii',
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) )
% 2.31/2.68 , ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.68 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z',
% 2.31/2.68 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 2.31/2.68 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.31/2.68 , 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.31/2.68 , 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.68 , clause( 20649, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.31/2.68 , 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20650, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.31/2.68 , 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20651, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.68 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_Complex_Oii', 'tc_Complex_Ocomplex'
% 2.31/2.68 ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20652, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.68 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.68 'c_HOL_Ominus__class_Ominus'( 'v_z', 'c_Complex_Oii',
% 2.31/2.68 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20653, [
% 2.31/2.68 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20654, [
% 2.31/2.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20655, [
% 2.31/2.68 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20656, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.31/2.68 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20657, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.68 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20658, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 2.31/2.68 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20659, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 2.31/2.68 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20660, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 2.31/2.68 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20661, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20662, [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20663, [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20664, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20665, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20666, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20667, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20668, [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20669, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20670, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20671, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20672, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20673, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20674, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20675, [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20676, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20677, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20678, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20679, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20680, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20681, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20682, [ 'class_Power_Opower'( 'tc_nat' ) ] )
% 2.31/2.68 , clause( 20683, [
% 2.31/2.68 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20684, [
% 2.31/2.68 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20685, [
% 2.31/2.68 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20686, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20687, [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20688, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20689, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20690, [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20691, [ 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20692, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20693, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20694, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20695, [ 'class_Ring__and__Field_Oordered__ring__strict'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20696, [ 'class_OrderedGroup_Opordered__ab__group__add'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20697, [ 'class_OrderedGroup_Olordered__ab__group__add'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20698, [ 'class_OrderedGroup_Oordered__ab__group__add'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20699, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20700, [ 'class_Ring__and__Field_Opordered__semiring'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20701, [ 'class_Ring__and__Field_Opordered__ring__abs'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20702, [ 'class_RealVector_Oreal__normed__algebra__1'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20703, [ 'class_Ring__and__Field_Oordered__semiring'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20704, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20705, [ 'class_Ring__and__Field_Odivision__by__zero'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20706, [ 'class_Ring__and__Field_Oordered__semidom'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20707, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20708, [ 'class_RealVector_Oreal__normed__algebra'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20709, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20710, [ 'class_RealVector_Oreal__normed__vector'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20711, [ 'class_OrderedGroup_Ocomm__monoid__mult'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20712, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20713, [ 'class_Ring__and__Field_Opordered__ring'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20714, [ 'class_Ring__and__Field_Oordered__field'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20715, [ 'class_Ring__and__Field_Olordered__ring'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20716, [ 'class_Ring__and__Field_Odivision__ring'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20717, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20718, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20719, [ 'class_Ring__and__Field_Ozero__neq__one'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20720, [ 'class_Ring__and__Field_Oordered__idom'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20721, [ 'class_Ring__and__Field_Omult__mono1'(
% 2.31/2.68 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20722, [ 'class_RealVector_Oreal__algebra__1'( 'tc_RealDef_Oreal'
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20723, [ 'class_OrderedGroup_Oab__group__add'( 'tc_RealDef_Oreal'
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20724, [ 'class_Ring__and__Field_Omult__zero'( 'tc_RealDef_Oreal'
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20725, [ 'class_Ring__and__Field_Omult__mono'( 'tc_RealDef_Oreal'
% 2.31/2.68 ) ] )
% 2.31/2.68 , clause( 20726, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_RealDef_Oreal' )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20727, [ 'class_Ring__and__Field_Osemiring'( 'tc_RealDef_Oreal' )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20728, [ 'class_RealVector_Ometric__space'( 'tc_RealDef_Oreal' )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20729, [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20730, [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20731, [ 'class_Ring__and__Field_Oring__1'( 'tc_RealDef_Oreal' )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20732, [ 'class_Ring__and__Field_Oabs__if'( 'tc_RealDef_Oreal' )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 20733, [ 'class_Ring__and__Field_Ofield'( 'tc_RealDef_Oreal' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20734, [ 'class_RealVector_Odist__norm'( 'tc_RealDef_Oreal' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20735, [ 'class_Ring__and__Field_Oring'( 'tc_RealDef_Oreal' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20736, [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 20737, [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20738, [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20739, [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20740, [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20741, [ 'class_Power_Opower'( 'tc_RealDef_Oreal' ) ] )
% 2.31/2.68 , clause( 20742, [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 2.31/2.68 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.68 , clause( 20743, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 2.31/2.68 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.68 , clause( 20744, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20745, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20746, [ 'class_RealVector_Oreal__normed__algebra__1'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20747, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20748, [ 'class_Ring__and__Field_Odivision__by__zero'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20749, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20750, [ 'class_RealVector_Oreal__normed__algebra'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20751, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20752, [ 'class_RealVector_Oreal__normed__vector'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20753, [ 'class_OrderedGroup_Ocomm__monoid__mult'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20754, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20755, [ 'class_Ring__and__Field_Odivision__ring'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20756, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20757, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20758, [ 'class_Ring__and__Field_Ozero__neq__one'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20759, [ 'class_RealVector_Oreal__algebra__1'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20760, [ 'class_OrderedGroup_Oab__group__add'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20761, [ 'class_Ring__and__Field_Omult__zero'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20762, [ 'class_OrderedGroup_Omonoid__mult'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20763, [ 'class_Ring__and__Field_Osemiring'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20764, [ 'class_RealVector_Ometric__space'( 'tc_Complex_Ocomplex'
% 2.31/2.69 ) ] )
% 2.31/2.69 , clause( 20765, [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex'
% 2.31/2.69 ) ] )
% 2.31/2.69 , clause( 20766, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex'
% 2.31/2.69 ) ] )
% 2.31/2.69 , clause( 20767, [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex'
% 2.31/2.69 ) ] )
% 2.31/2.69 , clause( 20768, [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' )
% 2.31/2.69 ] )
% 2.31/2.69 , clause( 20769, [ 'class_RealVector_Odist__norm'( 'tc_Complex_Ocomplex' )
% 2.31/2.69 ] )
% 2.31/2.69 , clause( 20770, [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' )
% 2.31/2.69 ] )
% 2.31/2.69 , clause( 20771, [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' )
% 2.31/2.69 ] )
% 2.31/2.69 , clause( 20772, [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 , clause( 20773, [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ] )
% 2.31/2.69 ] ).
% 2.31/2.69
% 2.31/2.69
% 2.31/2.69
% 2.31/2.69 eqswap(
% 2.31/2.69 clause( 21376, [ =( 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_Complex_Ocomplex' ),
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'c_RealVector_Odist__class_Odist'( X, Y,
% 2.31/2.69 'tc_Complex_Ocomplex' ) ) ] )
% 2.31/2.69 , clause( 20584, [ =( 'c_RealVector_Odist__class_Odist'( X, Y,
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_Complex_Ocomplex' ),
% 2.31/2.69 'tc_Complex_Ocomplex' ) ) ] )
% 2.31/2.69 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 2.31/2.69
% 2.31/2.69
% 2.31/2.69 subsumption(
% 2.31/2.69 clause( 488, [ =( 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_Complex_Ocomplex' ),
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'c_RealVector_Odist__class_Odist'( X, Y,
% 2.31/2.69 'tc_Complex_Ocomplex' ) ) ] )
% 2.31/2.69 , clause( 21376, [ =( 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_Complex_Ocomplex' ),
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'c_RealVector_Odist__class_Odist'( X, Y,
% 2.31/2.69 'tc_Complex_Ocomplex' ) ) ] )
% 2.31/2.69 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.31/2.69 )] ) ).
% 2.31/2.69
% 2.31/2.69
% 2.31/2.69 paramod(
% 2.31/2.69 clause( 23269, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.31/2.69 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 2.31/2.69 ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Ominus__class_Ominus'( 'v_z', 'c_Complex_Oii',
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) )
% 2.31/2.69 , ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.69 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z',
% 2.31/2.69 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 2.31/2.69 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.31/2.69 , 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.69 , clause( 488, [ =( 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_Complex_Ocomplex' ),
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'c_RealVector_Odist__class_Odist'( X, Y,
% 2.31/2.69 'tc_Complex_Ocomplex' ) ) ] )
% 2.31/2.69 , 0, clause( 20648, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Ominus__class_Ominus'( 'v_z', 'c_Complex_Oii',
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) )
% 2.31/2.69 , ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.69 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z',
% 2.31/2.69 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 2.31/2.69 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Ominus__class_Ominus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.31/2.69 , 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.31/2.69 , 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.69 , 2, 4, substitution( 0, [ :=( X, 'v_z' ), :=( Y, 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) )] ), substitution( 1, [] )).
% 2.31/2.69
% 2.31/2.69
% 2.31/2.69 paramod(
% 2.31/2.69 clause( 23271, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.31/2.69 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~(
% 2.31/2.69 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.69 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) )
% 2.31/2.69 , ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.69 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z',
% 2.31/2.69 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 2.31/2.69 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.31/2.69 , 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.69 , clause( 488, [ =( 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_Complex_Ocomplex' ),
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'c_RealVector_Odist__class_Odist'( X, Y,
% 2.31/2.69 'tc_Complex_Ocomplex' ) ) ] )
% 2.31/2.69 , 0, clause( 23269, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.31/2.69 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 2.31/2.69 ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Ominus__class_Ominus'( 'v_z', 'c_Complex_Oii',
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) )
% 2.31/2.69 , ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.69 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z',
% 2.31/2.69 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 2.31/2.69 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.31/2.69 , 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.69 , 1, 4, substitution( 0, [ :=( X, 'v_z' ), :=( Y, 'c_Complex_Oii' )] ),
% 2.31/2.69 substitution( 1, [] )).
% 2.31/2.69
% 2.31/2.69
% 2.31/2.69 subsumption(
% 2.31/2.69 clause( 544, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_Complex_Oii', 'tc_Complex_Ocomplex'
% 2.31/2.69 ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'(
% 2.31/2.69 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.69 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z',
% 2.31/2.69 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 2.31/2.69 ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'(
% 2.31/2.69 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.69 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_Complex_Oii',
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'(
% 2.31/2.69 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.69 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) )
% 2.31/2.69 ] )
% 2.31/2.69 , clause( 23271, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.31/2.69 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~(
% 2.31/2.69 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.69 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) )
% 2.31/2.69 , ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.31/2.69 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z',
% 2.31/2.69 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 2.31/2.69 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.31/2.69 , 'tc_RealDef_Oreal' ) ) ] )
% 2.31/2.69 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1, 3 ), ==>( 2
% 2.31/2.69 , 0 ), ==>( 3, 1 )] ) ).
% 2.31/2.69
% 2.31/2.69
% 2.31/2.69 subsumption(
% 2.31/2.69 clause( 545, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal'
% 2.31/2.69 ), 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z'
% 2.31/2.69 , 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ),
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ]
% 2.31/2.69 )
% 2.31/2.69 , clause( 20649, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.31/2.69 , 'tc_RealDef_Oreal' ) ] )
% 2.31/2.69 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.31/2.69
% 2.31/2.69
% 2.31/2.69 paramod(
% 2.31/2.69 clause( 25189, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.31/2.69 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 2.31/2.69 ), 'tc_RealDef_Oreal' ) ] )
% 2.31/2.69 , clause( 488, [ =( 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_Complex_Ocomplex' ),
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'c_RealVector_Odist__class_Odist'( X, Y,
% 2.31/2.69 'tc_Complex_Ocomplex' ) ) ] )
% 2.31/2.69 , 0, clause( 20650, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.31/2.69 'c_HOL_Ominus__class_Ominus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.31/2.69 , 'tc_RealDef_Oreal' ) ] )
% 2.31/2.69 , 0, 3, substitution( 0, [ :=( X, 'v_z' ), :=( Y, 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_Complex_Ocomplex' ) )] ), substitution( 1, [] )).
% 2.31/2.69
% 2.31/2.69
% 2.31/2.69 subsumption(
% 2.31/2.69 clause( 546, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal'
% 2.31/2.69 ), 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ]
% 2.31/2.69 )
% 2.31/2.69 , clause( 25189, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.31/2.69 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.31/2.69 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 2.35/2.70 ), 'tc_RealDef_Oreal' ) ] )
% 2.35/2.70 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.35/2.70
% 2.35/2.70
% 2.35/2.70 subsumption(
% 2.35/2.70 clause( 547, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal'
% 2.35/2.70 ), 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z'
% 2.35/2.70 , 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ),
% 2.35/2.70 'tc_RealDef_Oreal' ) ] )
% 2.35/2.70 , clause( 20651, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.35/2.70 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_Complex_Oii', 'tc_Complex_Ocomplex'
% 2.35/2.70 ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ] )
% 2.35/2.70 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.35/2.70
% 2.35/2.70
% 2.35/2.70 paramod(
% 2.35/2.70 clause( 27110, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.35/2.70 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ] )
% 2.35/2.70 , clause( 488, [ =( 'c_RealVector_Onorm__class_Onorm'(
% 2.35/2.70 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_Complex_Ocomplex' ),
% 2.35/2.70 'tc_Complex_Ocomplex' ), 'c_RealVector_Odist__class_Odist'( X, Y,
% 2.35/2.70 'tc_Complex_Ocomplex' ) ) ] )
% 2.35/2.70 , 0, clause( 20652, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.35/2.70 'c_HOL_Ominus__class_Ominus'( 'v_z', 'c_Complex_Oii',
% 2.35/2.70 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ]
% 2.35/2.70 )
% 2.35/2.70 , 0, 3, substitution( 0, [ :=( X, 'v_z' ), :=( Y, 'c_Complex_Oii' )] ),
% 2.35/2.70 substitution( 1, [] )).
% 2.35/2.70
% 2.35/2.70
% 2.35/2.70 subsumption(
% 2.35/2.70 clause( 548, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal'
% 2.35/2.70 ), 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_Complex_Oii',
% 2.35/2.70 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ] )
% 2.35/2.70 , clause( 27110, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.35/2.70 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ] )
% 2.35/2.70 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.35/2.70
% 2.35/2.70
% 2.35/2.70 resolution(
% 2.35/2.70 clause( 27111, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.35/2.70 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.35/2.70 , 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.35/2.70 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~(
% 2.35/2.70 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.35/2.70 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) )
% 2.35/2.70 ] )
% 2.35/2.70 , clause( 544, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.35/2.70 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_Complex_Oii', 'tc_Complex_Ocomplex'
% 2.35/2.70 ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'(
% 2.35/2.70 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.35/2.70 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Oplus__class_Oplus'( 'v_z',
% 2.35/2.70 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 2.35/2.70 ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'(
% 2.35/2.70 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.35/2.70 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_Complex_Oii',
% 2.35/2.70 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'(
% 2.35/2.70 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.35/2.70 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) )
% 2.35/2.70 ] )
% 2.35/2.70 , 0, clause( 547, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.35/2.70 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_Complex_Oii', 'tc_Complex_Ocomplex'
% 2.35/2.70 ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ] )
% 2.35/2.70 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 2.35/2.70
% 2.35/2.70
% 2.35/2.70 resolution(
% 2.35/2.70 clause( 27112, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.35/2.70 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~(
% 2.35/2.70 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.35/2.70 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) )
% 2.35/2.70 ] )
% 2.35/2.70 , clause( 27111, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.35/2.70 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.35/2.70 , 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.35/2.70 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~(
% 2.35/2.70 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.35/2.70 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) )
% 2.35/2.70 ] )
% 2.35/2.70 , 0, clause( 545, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Onorm__class_Onorm'(
% 2.35/2.70 'c_HOL_Oplus__class_Oplus'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.35/2.70 , 'tc_RealDef_Oreal' ) ] )
% 2.35/2.70 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 2.35/2.70
% 2.35/2.70
% 2.35/2.70 resolution(
% 2.35/2.70 clause( 27113, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.35/2.70 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 2.35/2.70 ), 'tc_RealDef_Oreal' ) ) ] )
% 2.35/2.70 , clause( 27112, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.35/2.70 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ), ~(
% 2.35/2.70 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_RealDef_Oreal' ),
% 2.35/2.70 'c_RealVector_Odist__class_Odist'( 'v_z', 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) )
% 2.35/2.70 ] )
% 2.35/2.70 , 0, clause( 548, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.35/2.70 'c_Complex_Oii', 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ] )
% 2.35/2.70 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 2.35/2.70
% 2.35/2.70
% 2.35/2.70 resolution(
% 2.35/2.70 clause( 27114, [] )
% 2.35/2.70 , clause( 27113, [ ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.35/2.70 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 2.35/2.70 ), 'tc_RealDef_Oreal' ) ) ] )
% 2.35/2.70 , 0, clause( 546, [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.70 'tc_RealDef_Oreal' ), 'c_RealVector_Odist__class_Odist'( 'v_z',
% 2.35/2.70 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex'
% 2.35/2.70 ), 'tc_RealDef_Oreal' ) ] )
% 2.35/2.70 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 2.35/2.70
% 2.35/2.70
% 2.35/2.70 subsumption(
% 2.35/2.70 clause( 20027, [] )
% 2.35/2.70 , clause( 27114, [] )
% 2.35/2.70 , substitution( 0, [] ), permutation( 0, [] ) ).
% 2.35/2.70
% 2.35/2.70
% 2.35/2.70 end.
% 2.35/2.70
% 2.35/2.70 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.35/2.70
% 2.35/2.70 Memory use:
% 2.35/2.70
% 2.35/2.70 space for terms: 500322
% 2.35/2.70 space for clauses: 864006
% 2.35/2.70
% 2.35/2.70
% 2.35/2.70 clauses generated: 81923
% 2.35/2.70 clauses kept: 20028
% 2.35/2.70 clauses selected: 522
% 2.35/2.70 clauses deleted: 146
% 2.35/2.70 clauses inuse deleted: 0
% 2.35/2.70
% 2.35/2.70 subsentry: 197104
% 2.35/2.70 literals s-matched: 117801
% 2.35/2.70 literals matched: 113755
% 2.35/2.70 full subsumption: 64551
% 2.35/2.70
% 2.35/2.70 checksum: -434700950
% 2.35/2.70
% 2.35/2.70
% 2.35/2.70 Bliksem ended
%------------------------------------------------------------------------------