TSTP Solution File: SWV582-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV582-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:26:53 EDT 2022
% Result : Timeout 300.05s 300.45s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWV582-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n006.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 : Tue Jun 14 23:39:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.21/1.61 *** allocated 10000 integers for termspace/termends
% 1.21/1.61 *** allocated 10000 integers for clauses
% 1.21/1.61 *** allocated 10000 integers for justifications
% 1.21/1.61 *** allocated 15000 integers for termspace/termends
% 1.21/1.61 *** allocated 22500 integers for termspace/termends
% 1.21/1.61 *** allocated 33750 integers for termspace/termends
% 1.21/1.61 Bliksem 1.12
% 1.21/1.61
% 1.21/1.61
% 1.21/1.61 Automatic Strategy Selection
% 1.21/1.61
% 1.21/1.61 Clauses:
% 1.21/1.61 [
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Y, X ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.21/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( U, W, V0, V1, V2, V3, V4 ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), Y ), Z ) ), T ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U
% 1.21/1.61 , W, V0, V1, V2, V3, V4 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X
% 1.21/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) )
% 1.21/1.61 ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( Y, Z, T, U, W, V0, V1 ) ),
% 1.21/1.61 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), V2 ), V3 ) ), V3 ), V2 ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( Y, Z, T, U, W, V0, V1 ) ),
% 1.21/1.61 =( V2, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), V2 ), V3 ) ), V3 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Y, X ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.21/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), Y ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( T, U, W, V0, V1, V2, V3 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W ), hAPP( Y, hAPP( X, W ) )
% 1.21/1.61 ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X
% 1.21/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), Y ), X
% 1.21/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X
% 1.21/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), Y ), X
% 1.21/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ), X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ), X ), Z ) ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( W, Y, X, V0, Z, V1, V2, V3 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, U ), Y ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), Y ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( W, Y, X, V0, Z, V1, V2, V3 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U
% 1.21/1.61 ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), W ) ) ), ~( hBOOL( hAPP( hAPP( X, U
% 1.21/1.61 ), T ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( V0, W, X, V1, Y, V2
% 1.21/1.61 , V3, V4 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, U ), Y ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), Y ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( W, Y, X, V0, Z, V1, V2, V3 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T
% 1.21/1.61 ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), W ) ) ), ~( hBOOL( hAPP( hAPP( X, U
% 1.21/1.61 ), Z ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( V0, W, X, V1, Y, V2
% 1.21/1.61 , V3, V4 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.21/1.61 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.21/1.61 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T )
% 1.21/1.61 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ),
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ),
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ),
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ),
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ),
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( T, X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ),
% 1.21/1.61 'c_RealVector_Oadditive'( 'c_HOL_Otimes__class_Otimes'( Y, X ), X, X ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.21/1.61 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), Y ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.21/1.61 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Z, X ), U ) ) ) ), =( T, U ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Y, X ), Y ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), Z ) ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.61 ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Y, X ), Y ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), Z ) ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.61 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), Y ), T ) ), Z ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U
% 1.21/1.61 , W, V0, V1, V2, V3, V4 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( U, W, V0, V1, V2, V3, V4 ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.21/1.61 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z
% 1.21/1.61 , X ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X
% 1.21/1.61 ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.61 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T
% 1.21/1.61 , X ), Z ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z
% 1.21/1.61 ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z
% 1.21/1.61 , X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.21/1.61 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T
% 1.21/1.61 ), X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.61 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.21/1.61 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Osemigroup__mult'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.61 , Z ), X ), T ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Z, X ), T ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.61 , Y ), Z ), X ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), Z ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, X ), X ), Z ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.21/1.61 T, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.21/1.61 T, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), Z ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, X ), X ), Z ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Z, X ), T ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Osemigroup__mult'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.61 , Z ), X ), T ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.61 , Y ), Z ), X ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.61 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oinverse__class_Odivide'( Y
% 1.21/1.61 , Z, X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.61 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.21/1.61 , Y, X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.61 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oinverse__class_Odivide'( Y
% 1.21/1.61 , Z, X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.61 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.21/1.61 , Y, X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.21/1.61 ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.21/1.61 ) ) ) ],
% 1.21/1.61 [ 'c_Finite__Set_Ofinite'( 'c_SetInterval_Oord__class_OatMost'( X,
% 1.21/1.61 'tc_nat' ), 'tc_nat' ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Y ), Y ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Z ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ) ), ~(
% 1.21/1.61 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.21/1.61 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.21/1.61 , Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.21/1.61 ), T ), X ), Z ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( U, W, V0
% 1.21/1.61 , V1, V2, V3, V4, V5 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.21/1.61 ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), T ), Z ) ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.21/1.61 , Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X )
% 1.21/1.61 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ), X ), Z ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( =( hAPP( X, hAPP( Y, Z ) ), hAPP( T, hAPP( U, W ) ) ) ), =( hAPP(
% 1.21/1.61 'c_Fun_Ocomp'( X, Y, V0, V1, V2 ), Z ), hAPP( 'c_Fun_Ocomp'( T, U, V3, V1
% 1.21/1.61 , V4 ), W ) ) ],
% 1.21/1.61 [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( W, V0, V1, T, U )
% 1.21/1.61 ) ), =( hAPP( X, hAPP( Y, V2 ) ), hAPP( W, hAPP( V0, V2 ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Y, X ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), Z ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.21/1.61 , X ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), T ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), U ), X ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.21/1.61 'class_RealVector_Oreal__normed__vector'( Y ) ), ~(
% 1.21/1.61 'class_RealVector_Oreal__normed__vector'( Z ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( Y ), hAPP( hAPP( T, U ), W ) ), hAPP( hAPP(
% 1.21/1.61 T, V0 ), V1 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( Y ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( Y ), hAPP( hAPP( T, hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( Z ), U ), V0 ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), W ), V1 ) ) ), hAPP( hAPP( T, hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( Z ), U ), V0 ) ), V1 ) ) ), hAPP(
% 1.21/1.61 hAPP( T, V0 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), W ), V1 ) )
% 1.21/1.61 ) ), ~( 'c_RealVector_Obounded__bilinear'( T, Z, X, Y ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.21/1.61 X ) ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.21/1.61 X ) ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.21/1.61 , Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) )
% 1.21/1.61 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ =( 'c_Option_Ooption_Ooption__case'( X, Y, 'c_Option_Ooption_ONone'( Z
% 1.21/1.61 ), T, Z ), X ) ],
% 1.21/1.61 [ =( 'c_SetInterval_Oord__class_OlessThan'( hAPP( 'c_Suc', X ), 'tc_nat'
% 1.21/1.61 ), 'c_SetInterval_Oord__class_OatMost'( X, 'tc_nat' ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =( hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), Z ) ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =( hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), Z ) ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), =( Z, Y ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ),
% 1.21/1.61 Y ) ) ) ],
% 1.21/1.61 [ =( X, Y ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ), ~(
% 1.21/1.61 hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ), =( Y, X ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ), =( Y, X ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Z, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.21/1.61 Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), =( Z, Y ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Z, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.21/1.61 Z ) ) ) ],
% 1.21/1.61 [ =( 'c_HOL_Oord__class_Oless'( 'v_n', 'tc_nat' ), 'c_lessequals'( hAPP(
% 1.21/1.61 'c_Suc', 'v_n' ), 'tc_nat' ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =( hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), Y ), Y, X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), Y ), Y, X ), Z ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, T ), U ) )
% 1.21/1.61 , hAPP( hAPP( X, Z ), U ) ), =( T, W ), =( U, W ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( V0, X, V1, Y, V2, V3, W, V4, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.21/1.61 , hAPP( hAPP( X, Z ), U ) ), =( T, W ), =( U, W ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( V0, X, V1, Y, V2, V3, W, V4, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), Z ) )
% 1.21/1.61 , hAPP( hAPP( X, T ), U ) ), =( Z, W ), =( U, W ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( V0, X, V1, Y, V2, V3, W, V4, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.21/1.61 , hAPP( hAPP( X, T ), U ) ), =( Z, W ), =( U, W ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( V0, X, V1, Y, V2, V3, W, V4, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( X, U ),
% 1.21/1.61 T ) ), =( Y, W ), =( T, W ), ~( 'c_Ring__and__Field_Ofield'( V0, X, U, Z
% 1.21/1.61 , V1, V2, W, V3, V4 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( X, U ),
% 1.21/1.61 T ) ), =( T, W ), =( Y, W ), ~( 'c_Ring__and__Field_Ofield'( V0, X, U, Z
% 1.21/1.61 , V1, V2, W, V3, V4 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.21/1.61 hAPP( X, Y ), T ) ), U ) ), ~( 'c_Ring__and__Field_Ofield'( W, Z, V0, X,
% 1.21/1.61 V1, V2, V3, V4, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.61 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Ring__and__Field_Ofield'( W, Y, V0, X,
% 1.21/1.61 V1, V2, V3, V4, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.61 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( W, X, V0, V1, Y, V2, V3, V4, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.61 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( W, X, V0, V1, V2, V3, V4, Y, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.21/1.61 T ) ), ~( 'c_Ring__and__Field_Ofield'( U, Y, W, V0, V1, X, V2, V3, V4 ) )
% 1.21/1.61 ],
% 1.21/1.61 [ =( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( X, Z, T, U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), T ), hAPP( Y, hAPP( hAPP( X, Z ), T
% 1.21/1.61 ) ) ), ~( 'c_Ring__and__Field_Ofield'( U, X, W, V0, V1, Y, V2, V3, V4 )
% 1.21/1.61 ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Ring__and__Field_Ofield'( T, X
% 1.21/1.61 , U, W, V0, V1, Y, V2, V3 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( T, Y ), hAPP( U, Z ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( U, X, W, T, V0, V1, V2, V3, V4 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), W ) )
% 1.21/1.61 , hAPP( hAPP( Y, hAPP( hAPP( X, hAPP( hAPP( V0, Z ), W ) ), hAPP( hAPP(
% 1.21/1.61 V0, U ), T ) ) ), hAPP( hAPP( V0, T ), W ) ) ), =( W, V1 ), =( T, V1 ),
% 1.21/1.61 ~( 'c_Ring__and__Field_Ofield'( V2, Y, V3, V0, X, V4, V1, V5, V6 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, T ) ), hAPP( hAPP( U, hAPP(
% 1.21/1.61 hAPP( U, hAPP( hAPP( X, Z ), T ) ), hAPP( Y, Z ) ) ), hAPP( Y, T ) ) ),
% 1.21/1.61 =( T, W ), =( Z, W ), ~( 'c_Ring__and__Field_Ofield'( Y, V0, V1, U, V2,
% 1.21/1.61 V3, W, X, V4 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), W ) )
% 1.21/1.61 , hAPP( hAPP( Y, hAPP( hAPP( X, hAPP( hAPP( V0, Z ), W ) ), hAPP( hAPP(
% 1.21/1.61 V0, U ), T ) ) ), hAPP( hAPP( V0, T ), W ) ) ), =( W, V1 ), =( T, V1 ),
% 1.21/1.61 ~( 'c_Ring__and__Field_Ofield'( V2, Y, V3, V0, V4, V5, V1, X, V6 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Ring__and__Field_Ofield'( T, X
% 1.21/1.61 , Z, U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.21/1.61 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Ring__and__Field_Ofield'( U, W, V0, X
% 1.21/1.61 , V1, V2, V3, V4, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( T, U, W, X, V0, V1, V2, V3, V4 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.21/1.61 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Ring__and__Field_Ofield'( U, W, V0, X
% 1.21/1.61 , V1, V2, V3, V4, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.21/1.61 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Ring__and__Field_Ofield'( U, W, V0, V1
% 1.21/1.61 , V2, V3, V4, X, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( T, U, W, V0, V1, V2, V3, X, V4 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.21/1.61 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Ring__and__Field_Ofield'( U, W, V0, V1
% 1.21/1.61 , V2, V3, V4, X, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( Z, T ) ), hAPP( hAPP( U, Y ), T ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( W, V0, V1, V2, U, Z, V3, X, V4 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), T ), hAPP( hAPP( U, T ), Z ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( W, V0, V1, V2, U, Y, V3, X, V4 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.21/1.61 hAPP( X, Y ), T ) ), U ) ), ~( 'c_Ring__and__Field_Ofield'( W, V0, V1, V2
% 1.21/1.61 , Z, V3, V4, X, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.61 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Ring__and__Field_Ofield'( W, V0, V1, V2
% 1.21/1.61 , Y, V3, V4, X, V5 ) ) ],
% 1.21/1.61 [ ~( 'c_Ring__and__Field_Ofield'( X, Y, Z, T, U, W, V0, V1, V2 ) ), =(
% 1.21/1.61 V3, hAPP( hAPP( V1, hAPP( hAPP( U, V3 ), V4 ) ), V4 ) ) ],
% 1.21/1.61 [ ~( 'c_Ring__and__Field_Ofield'( X, Y, Z, T, U, W, V0, V1, V2 ) ), =(
% 1.21/1.61 hAPP( hAPP( U, hAPP( hAPP( V1, V3 ), V4 ) ), V4 ), V3 ) ],
% 1.21/1.61 [ ~( 'c_Ring__and__Field_Ofield'( X, Y, Z, T, U, W, V0, V1, V2 ) ), =(
% 1.21/1.61 hAPP( hAPP( V1, hAPP( hAPP( U, V3 ), V4 ) ), V4 ), V3 ) ],
% 1.21/1.61 [ ~( 'c_Ring__and__Field_Ofield'( X, Y, Z, T, U, W, V0, V1, V2 ) ), =(
% 1.21/1.61 V3, hAPP( hAPP( U, hAPP( hAPP( V1, V3 ), V4 ) ), V4 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.21/1.61 hAPP( hAPP( U, Z ), T ) ) ), ~( 'c_Ring__and__Field_Ofield'( W, V0, V1,
% 1.21/1.61 V2, X, V3, V4, U, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.21/1.61 hAPP( U, Y ), T ) ), Z ) ), ~( 'c_Ring__and__Field_Ofield'( W, V0, V1, V2
% 1.21/1.61 , X, V3, V4, U, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.61 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( W, V0, V1, X, V2, V3, V4, Y, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.21/1.61 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( W, V0, V1, X, V2, V3, V4, Z, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.21/1.61 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( W, V0, V1, X, Z, V2, V3, V4, V5 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.61 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( W, V0, V1, X, Y, V2, V3, V4, V5 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.21/1.61 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ), X ), Z ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.21/1.61 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X
% 1.21/1.61 ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), T ), Z ) ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z
% 1.21/1.61 ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), Z ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.61 , Z ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( T, X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ), U ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.61 , Z ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Z, X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.61 , Z ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.61 , T ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), U ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.21/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.21/1.61 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.21/1.61 'c_Finite__Set_Osetsum'( Y, Z, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.21/1.61 , 'c_Finite__Set_Ofinite'( Z, T ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.21/1.61 'c_Finite__Set_Osetsum'( Y, Z, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.21/1.61 , 'c_Finite__Set_Ofinite'( Z, T ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.21/1.61 ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.21/1.61 ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.21/1.61 , X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z )
% 1.21/1.61 , X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.21/1.61 , X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ), X
% 1.21/1.61 ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ), X ), Y ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X )
% 1.21/1.61 , Z ) ) ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP(
% 1.21/1.61 T, Y ), Z ) ), U ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( T
% 1.21/1.61 , W, U, V0, V1, X, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, Z ), T ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( Y,
% 1.21/1.61 W, U, V0, V1, X, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.21/1.61 T ), Z ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U, Y, T, W,
% 1.21/1.61 V0, X, V1 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( T, Z
% 1.21/1.61 ) ), Y ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U, T, Y, W
% 1.21/1.61 , V0, X, V1 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.21/1.61 T ), Y ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U, Z, Y, W,
% 1.21/1.61 V0, X, V1 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Z ), hAPP(
% 1.21/1.61 T, Y ) ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U, T, Z, W,
% 1.21/1.61 V0, X, V1 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, T ), Z ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U,
% 1.21/1.61 Y, W, V0, V1, X, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( T, Z
% 1.21/1.61 ) ), hAPP( T, Y ) ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'(
% 1.21/1.61 U, T, W, V0, V1, X, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP(
% 1.21/1.61 T, Y ), Z ) ), U ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( T
% 1.21/1.61 , W, U, V0, X, V1, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, Z ), T ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( Y,
% 1.21/1.61 W, U, V0, X, V1, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.21/1.61 T ), Z ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U, Y, T, W,
% 1.21/1.61 X, V0, V1 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( T, Z
% 1.21/1.61 ) ), Y ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U, T, Y, W
% 1.21/1.61 , X, V0, V1 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.21/1.61 T ), Y ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U, Z, Y, W,
% 1.21/1.61 X, V0, V1 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Z ), hAPP(
% 1.21/1.61 T, Y ) ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U, T, Z, W,
% 1.21/1.61 X, V0, V1 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.21/1.61 Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) )
% 1.21/1.61 ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( T, X ), U ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( T, X ), U ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Z, X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, X ), T
% 1.21/1.61 ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( U, X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), Y
% 1.21/1.61 ) ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 Y, X ), Z ) ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), =( X, Y
% 1.21/1.61 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.21/1.61 [ =( X, Y ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y )
% 1.21/1.61 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), =( X, Y
% 1.21/1.61 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 Y, X ), Z ) ) ), =( Y, Z ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), Z ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 Y, X ), Z ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 Y, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 Y, X ), Z ) ) ), =( Z, Y ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( T, X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.61 , Z ), X ), T ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.61 , Z ), X ), T ), hAPP( 'c_HOL_Otimes__class_Otimes'( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ), X ), Z ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.61 , Z ), X ), T ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Z, X ), T ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ), T ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Z, X ), T ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Z, X ), T ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ), T ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.61 ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( U, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), U ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.61 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.21/1.61 Z, X ) ), 'c_HOL_Oinverse__class_Odivide'( Y, hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.21/1.61 Z, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), Y ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), Y ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y ) ), =( Y,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.21/1.61 ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.21/1.61 ), Y ), Z ), X ), T ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y
% 1.21/1.61 , X ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ =( 'c_Map_Omap__comp'( X, Y, 'v_k', Z, T, 't_a' ),
% 1.21/1.61 'c_Option_Ooption_Ooption__case'( 'c_Option_Ooption_ONone'( T ), X, hAPP(
% 1.21/1.61 Y, 'v_k' ), 'tc_Option_Ooption'( T ), Z ) ) ],
% 1.21/1.61 [ ~( =( hAPP( X, Y ), 'c_Option_Ooption_ONone'( Z ) ) ), =(
% 1.21/1.61 'c_Map_Omap__comp'( T, X, Y, Z, U, W ), 'c_Option_Ooption_ONone'( U ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( =( hAPP( X, Y ), 'c_Option_Ooption_ONone'( Z ) ) ), =(
% 1.21/1.61 'c_Map_Omap__comp'( T, X, Y, Z, U, W ), 'c_Option_Ooption_ONone'( U ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.21/1.61 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.21/1.61 X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), U ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), U ), X ) ), =( U,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.21/1.61 ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.21/1.61 Y ), X ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.21/1.61 Y ), X ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Y, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Y, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.21/1.61 Y ), X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Y ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.21/1.61 Y ), X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ),
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~(
% 1.21/1.61 hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ),
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~(
% 1.21/1.61 hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.21/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.61 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.61 X ), Z ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.61 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z
% 1.21/1.61 ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.61 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z
% 1.21/1.61 ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.21/1.61 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.61 X ), T ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.21/1.61 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y
% 1.21/1.61 , X ), T ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ), X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.21/1.61 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y
% 1.21/1.61 , X ), T ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ), X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.21/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), Y ), Z ) ), T ) ), ~( 'c_Ring__and__Field_Opordered__ring'( U, W, V0
% 1.21/1.61 , V1, V2, V3, V4, V5 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( T, U, W, V0, V1, V2 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.61 ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) )
% 1.21/1.61 , ~( 'c_Ring__and__Field_Oring'( T, U, W, V0, V1, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ), ~(
% 1.21/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), hAPP( 'c_Suc', X )
% 1.21/1.61 ) ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.21/1.61 Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ =( X, hAPP( 'c_Suc', Y ) ), hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' )
% 1.21/1.61 , Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( 'c_Suc', Y
% 1.21/1.61 ) ) ) ) ],
% 1.21/1.61 [ 'c_Finite__Set_Ofinite'(
% 1.21/1.61 'c_SetInterval_Oord__class_OgreaterThanLessThan'( X, Y, 'tc_nat' ),
% 1.21/1.61 'tc_nat' ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.61 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z
% 1.21/1.61 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Y ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.61 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), Y ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( T, X ), Y ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), T
% 1.21/1.61 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.21/1.61 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.21/1.61 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.21/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Z, X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ), X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ), X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'class_OrderedGroup_Oab__group__add'( Y ) ), =( hAPP( Z, hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( Y ), hAPP( Z, T ) ), hAPP( Z, U ) ) ), ~(
% 1.21/1.61 'c_RealVector_Oadditive'( Z, X, Y ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.21/1.61 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ),
% 1.21/1.61 'c_RealVector_Oadditive'( 'c_RealVector_OscaleR__class_OscaleR'( Y, X ),
% 1.21/1.61 X, X ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.21/1.61 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 T, X ), Z ) ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.21/1.61 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Y, X ), T ) ), T, X ) ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.61 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.21/1.61 'c_RealVector_Ovector__space'( Z, X, Y ) ), =( hAPP( hAPP( Z,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), T ), 'c_HOL_Ozero__class_Ozero'( Y ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.61 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.21/1.61 'c_RealVector_Ovector__space'( Z, X, Y ) ), =( hAPP( hAPP( Z, T ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( Y ) ), 'c_HOL_Ozero__class_Ozero'( Y ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Ofield'( Y ) ), =( hAPP( hAPP( Z,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( Y ) ), T ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.21/1.61 , ~( 'c_RealVector_Ovector__space'( Z, Y, X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Ofield'( Y ) ), =( hAPP( hAPP( Z, hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( Y ), T ) ), U ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( Z, T ), U ) ) ), ~(
% 1.21/1.61 'c_RealVector_Ovector__space'( Z, Y, X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Ofield'( Y ) ), =( hAPP( hAPP( Z, T ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.21/1.61 'c_RealVector_Ovector__space'( Z, Y, X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.61 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.21/1.61 'c_RealVector_Ovector__space'( Z, X, Y ) ), =( hAPP( hAPP( Z,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), T ), hAPP( hAPP( Z,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), U ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Ofield'( Y ) ), =( hAPP( hAPP( Z, T ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), U ) ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( Z, T ), U ) ) ), ~(
% 1.21/1.61 'c_RealVector_Ovector__space'( Z, Y, X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.61 'class_OrderedGroup_Oab__group__add'( Y ) ), ~(
% 1.21/1.61 'c_RealVector_Ovector__space'( Z, X, Y ) ), =( hAPP( hAPP( Z, T ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( Y ) ), hAPP( hAPP( Z, U ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.21/1.61 hAPP( Y, T ) ), Z ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U
% 1.21/1.61 , Y, W, V0, V1, X, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.21/1.61 hAPP( Y, T ) ), Z ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U
% 1.21/1.61 , Y, W, V0, V1, X, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.21/1.61 T ), hAPP( Z, Y ) ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U
% 1.21/1.61 , Z, W, V0, V1, X, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.21/1.61 T ), hAPP( Z, Y ) ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U
% 1.21/1.61 , Z, W, V0, V1, X, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( T, Z
% 1.21/1.61 ) ), hAPP( T, Y ) ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'(
% 1.21/1.61 U, T, W, V0, X, V1, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, T ), Z ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U,
% 1.21/1.61 Y, W, V0, X, V1, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.21/1.61 hAPP( Y, T ) ), Z ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U
% 1.21/1.61 , Y, W, V0, X, V1, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.21/1.61 hAPP( Y, T ) ), Z ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U
% 1.21/1.61 , Y, W, V0, X, V1, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, hAPP( hAPP( W, Y ), U ) ), T ) ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( Z, V0, V1, W, V2, X, V3 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, Z ), hAPP( hAPP( W, U ), T ) ) ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( W, V0, V1, Y, V2, X, V3 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.21/1.61 T ), hAPP( Z, Y ) ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U
% 1.21/1.61 , Z, W, V0, X, V1, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.21/1.61 T ), hAPP( Z, Y ) ) ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'( U
% 1.21/1.61 , Z, W, V0, X, V1, V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, Z ), hAPP( hAPP( W, U ), T ) ) ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( Y, V0, V1, W, V2, X, V3 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, hAPP( hAPP( W, Y ), U ) ), T ) ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( W, V0, V1, Z, V2, X, V3 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, hAPP( hAPP( W, Y ), U ) ), T ) ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( Z, V0, V1, W, X, V2, V3 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, Z ), hAPP( hAPP( W, U ), T ) ) ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( W, V0, V1, Y, X, V2, V3 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, Z ), hAPP( hAPP( W, U ), T ) ) ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( Y, V0, V1, W, X, V2, V3 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, hAPP( hAPP( W, Y ), U ) ), T ) ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( W, V0, V1, Z, X, V2, V3 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Y ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), Z ) ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( Y, Z, T, U, W, V0, V1 ) ),
% 1.21/1.61 =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), V2 ), V3 ) ), V3 ), V2 ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( Y, Z, T, U, W, V0, V1 ) ),
% 1.21/1.61 =( V2, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), V2 ), V3 ) ), V3 ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.21/1.61 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.21/1.61 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), Y ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ), X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.21/1.61 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.21/1.61 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.61 ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.61 ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.21/1.61 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( W, V0, V1, Z, X, V2 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.61 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( W, V0, V1, Y, X, V2 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.21/1.61 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Ring__and__Field_Oring'( U, W, V0, V1
% 1.21/1.61 , X, V2 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.21/1.61 hAPP( U, Y ), T ) ), Z ) ), ~( 'c_Ring__and__Field_Oring'( X, W, V0, U,
% 1.21/1.61 V1, V2 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.21/1.61 hAPP( hAPP( U, Z ), T ) ) ), ~( 'c_Ring__and__Field_Oring'( X, W, V0, U,
% 1.21/1.61 V1, V2 ) ) ],
% 1.21/1.61 [ ~( 'c_Ring__and__Field_Oring'( X, Y, Z, T, U, W ) ), =( V0, hAPP( hAPP(
% 1.21/1.61 X, hAPP( hAPP( T, V0 ), V1 ) ), V1 ) ) ],
% 1.21/1.61 [ ~( 'c_Ring__and__Field_Oring'( X, Y, Z, T, U, W ) ), =( hAPP( hAPP( T
% 1.21/1.61 , hAPP( hAPP( X, V0 ), V1 ) ), V1 ), V0 ) ],
% 1.21/1.61 [ ~( 'c_Ring__and__Field_Oring'( X, Y, Z, T, U, W ) ), =( hAPP( hAPP( X
% 1.21/1.61 , hAPP( hAPP( T, V0 ), V1 ) ), V1 ), V0 ) ],
% 1.21/1.61 [ ~( 'c_Ring__and__Field_Oring'( X, Y, Z, T, U, W ) ), =( V0, hAPP( hAPP(
% 1.21/1.61 T, hAPP( hAPP( X, V0 ), V1 ) ), V1 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.61 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Ring__and__Field_Oring'( Y, W, V0, X,
% 1.21/1.61 V1, V2 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.21/1.61 hAPP( X, Y ), T ) ), U ) ), ~( 'c_Ring__and__Field_Oring'( Z, W, V0, X,
% 1.21/1.61 V1, V2 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), T ), hAPP( hAPP( U, T ), Z ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( U, Y, W, X, V0, V1 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( Z, T ) ), hAPP( hAPP( U, Y ), T ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( U, Z, W, X, V0, V1 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.21/1.61 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Ring__and__Field_Oring'( U, W, V0, X,
% 1.21/1.61 V1, V2 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( T, U, W, X, V0, V1 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.21/1.61 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Ring__and__Field_Oring'( U, W, V0, X,
% 1.21/1.61 V1, V2 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.21/1.61 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( Z, W, V0, V1, X, V2 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), T ), hAPP( hAPP( X, Z ), hAPP( Y, T
% 1.21/1.61 ) ) ), ~( 'c_Ring__and__Field_Oring'( U, Y, W, V0, X, V1 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.61 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( Y, W, V0, V1, X, V2 ) ) ],
% 1.21/1.61 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), hAPP( X, T
% 1.21/1.61 ) ) ), ~( 'c_Ring__and__Field_Oring'( U, X, W, V0, Y, V1 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, T ) ), hAPP( hAPP( X, Z ),
% 1.21/1.61 T ) ), ~( 'c_Ring__and__Field_Oring'( U, Y, W, V0, X, V1 ) ) ],
% 1.21/1.61 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.21/1.61 T ) ), ~( 'c_Ring__and__Field_Oring'( U, X, W, V0, Y, V1 ) ) ],
% 1.21/1.61 [ ~( 'c_Ring__and__Field_Oring'( X, Y, Z, T, U, W ) ), =( hAPP( hAPP( T
% 1.21/1.61 , hAPP( hAPP( U, V0 ), V1 ) ), hAPP( hAPP( T, hAPP( hAPP( U, hAPP( hAPP(
% 1.21/1.61 X, V2 ), V0 ) ), V1 ) ), V3 ) ), hAPP( hAPP( T, hAPP( hAPP( U, V2 ), V1 )
% 1.21/1.61 ), V3 ) ) ],
% 1.21/1.61 [ ~( 'c_Ring__and__Field_Oring'( X, Y, Z, T, U, W ) ), =( hAPP( hAPP( T
% 1.21/1.61 , hAPP( hAPP( U, V0 ), V1 ) ), V2 ), hAPP( hAPP( T, hAPP( hAPP( U, V3 ),
% 1.21/1.61 V1 ) ), hAPP( hAPP( T, hAPP( hAPP( U, hAPP( hAPP( X, V0 ), V3 ) ), V1 ) )
% 1.21/1.61 , V2 ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.21/1.61 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.21/1.61 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), =( Z,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), =( Y,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.21/1.61 , Y ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.21/1.61 X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Y ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), Z ) ) ), =( Y, hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), =( Y, Z ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), T ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( T, X
% 1.21/1.61 ), Y ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T
% 1.21/1.61 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Y
% 1.21/1.61 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), T ), X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.61 ), X ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ), X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ), T )
% 1.21/1.61 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ), X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.61 ), X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) )
% 1.21/1.61 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ), X ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Y ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), Z ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ), T ), X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( U, X
% 1.21/1.61 ), Z ) ), W ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ), X ), Z ) ), W ) ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.21/1.61 ), Z ), T ), X ), U ) ), W ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 T, X ), U ) ), Y ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), U ) ), W ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ), T ), X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( U, X
% 1.21/1.61 ), Z ) ), W ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ), X ), Z ) ), T ), X ),
% 1.21/1.61 W ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.21/1.61 ), Y ), Z ), X ), T ) ), U ), X ), W ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ), U ), X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.21/1.61 ), T ) ), W ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X
% 1.21/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( Y, Z, T, U, W, V0 ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.21/1.61 X ), V1 ), V2 ) ), V2 ), V1 ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( Y, Z, T, U, W, V0 ) ), =( V1, hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.21/1.61 X ), V1 ), V2 ) ), V2 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.21/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.21/1.61 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.21/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.21/1.61 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), Y ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( T, U, W, V0, V1, V2 ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =( hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =( hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.21/1.61 ), T ), Y ), X ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ), U ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Z ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ) ), ~(
% 1.21/1.61 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.21/1.61 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ), X ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), U )
% 1.21/1.61 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.61 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), T ), Z, X ),
% 1.21/1.61 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.61 , T ), Z, X ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.21/1.61 'class_RealVector_Oreal__normed__vector'( Y ) ), ~(
% 1.21/1.61 'class_RealVector_Oreal__normed__vector'( Z ) ), 'c_RealVector_Oadditive'(
% 1.21/1.61 hAPP( T, U ), Y, Z ), ~( 'c_RealVector_Obounded__bilinear'( T, X, Y, Z )
% 1.21/1.61 ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.61 ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.61 ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.61 ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.61 ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) )
% 1.21/1.61 , ~( 'c_Ring__and__Field_Ofield'( T, U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( T, U, W, V0, V1, V2, V3, V4, V5 ) ) ],
% 1.21/1.61 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.21/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.21/1.61 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ),
% 1.21/1.61 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.21/1.61 ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.21/1.61 ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ 'c_Finite__Set_Ofinite'( 'c_SetInterval_Oord__class_OlessThan'( X,
% 1.21/1.61 'tc_nat' ), 'tc_nat' ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, hAPP( hAPP( W, Y ), U ) ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( W, V0, X, V1, V2, Z, V3, V4 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, Z ), hAPP( hAPP( W, U ), T ) ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( Y, V0, X, V1, V2, W, V3, V4 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, Z ), hAPP( hAPP( W, U ), T ) ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( W, V0, X, V1, V2, Y, V3, V4 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, hAPP( hAPP( W, Y ), U ) ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( Z, V0, X, V1, V2, W, V3, V4 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, hAPP( hAPP( W, Y ), U ) ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( W, V0, V1, X, V2, Z, V3, V4 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, Z ), hAPP( hAPP( W, U ), T ) ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( Y, V0, V1, X, V2, W, V3, V4 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, Z ), hAPP( hAPP( W, U ), T ) ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( W, V0, V1, X, V2, Y, V3, V4 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, hAPP( hAPP( W, Y ), U ) ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( Z, V0, V1, X, V2, W, V3, V4 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP( Z, hAPP( hAPP( T, U )
% 1.21/1.61 , W ) ), V0 ) ), V1 ) ), V2 ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y,
% 1.21/1.61 hAPP( hAPP( Z, U ), V0 ) ), V1 ) ), hAPP( hAPP( Y, hAPP( hAPP( Z, W ), V0
% 1.21/1.61 ) ), V2 ) ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( Y, V3, X, V4,
% 1.21/1.61 Z, T, V5, V6 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP( Z, T ), U ) ), W ) )
% 1.21/1.61 , hAPP( hAPP( Y, hAPP( hAPP( Z, V0 ), U ) ), V1 ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, hAPP( hAPP( Y, hAPP( hAPP( Z, hAPP( hAPP( V2, T ), V0 ) ), U ) )
% 1.21/1.61 , W ) ), V1 ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( Y, V3, X, V4
% 1.21/1.61 , Z, V2, V5, V6 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP( U
% 1.21/1.61 , W ), V0 ) ), V1 ) ), V2 ) ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( Z,
% 1.21/1.61 hAPP( hAPP( T, V0 ), V1 ) ), Y ) ), hAPP( hAPP( Z, hAPP( hAPP( T, W ), V1
% 1.21/1.61 ) ), V2 ) ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( Z, V3, X, V4,
% 1.21/1.61 T, U, V5, V6 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP( Z, T ), U ) ), W ) )
% 1.21/1.61 , hAPP( hAPP( Y, hAPP( hAPP( Z, V0 ), U ) ), V1 ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, W ), hAPP( hAPP( Y, hAPP( hAPP( Z, hAPP( hAPP( V2, V0 ), T ) ),
% 1.21/1.61 U ) ), V1 ) ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( Y, V3, X, V4
% 1.21/1.61 , Z, V2, V5, V6 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP( Z, hAPP( hAPP( T, U )
% 1.21/1.61 , W ) ), V0 ) ), V1 ) ), V2 ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y,
% 1.21/1.61 hAPP( hAPP( Z, U ), V0 ) ), V1 ) ), hAPP( hAPP( Y, hAPP( hAPP( Z, W ), V0
% 1.21/1.61 ) ), V2 ) ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( Y, V3, V4, X,
% 1.21/1.61 Z, T, V5, V6 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP( Z, T ), U ) ), W ) )
% 1.21/1.61 , hAPP( hAPP( Y, hAPP( hAPP( Z, V0 ), U ) ), V1 ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, hAPP( hAPP( Y, hAPP( hAPP( Z, hAPP( hAPP( V2, T ), V0 ) ), U ) )
% 1.21/1.61 , W ) ), V1 ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( Y, V3, V4, X
% 1.21/1.61 , Z, V2, V5, V6 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP( U
% 1.21/1.61 , W ), V0 ) ), V1 ) ), V2 ) ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( Z,
% 1.21/1.61 hAPP( hAPP( T, V0 ), V1 ) ), Y ) ), hAPP( hAPP( Z, hAPP( hAPP( T, W ), V1
% 1.21/1.61 ) ), V2 ) ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( Z, V3, V4, X,
% 1.21/1.61 T, U, V5, V6 ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP( Z, T ), U ) ), W ) )
% 1.21/1.61 , hAPP( hAPP( Y, hAPP( hAPP( Z, V0 ), U ) ), V1 ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 hAPP( X, W ), hAPP( hAPP( Y, hAPP( hAPP( Z, hAPP( hAPP( V2, V0 ), T ) ),
% 1.21/1.61 U ) ), V1 ) ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( Y, V3, V4, X
% 1.21/1.61 , Z, V2, V5, V6 ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X
% 1.21/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X
% 1.21/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X
% 1.21/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X
% 1.21/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X
% 1.21/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X
% 1.21/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.21/1.61 ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.21/1.61 ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( Y, Z, T, U, W, V0, V1, V2 ) ), =(
% 1.21/1.61 V3, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), V3 ), V4 ) ), V4 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( Y, Z, T, U, W, V0, V1, V2 ) ), =(
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), V3 ), V4 ) ), V4 ), V3 ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.21/1.61 ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.21/1.61 ), 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.21/1.61 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.21/1.61 Z, X ) ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.21/1.61 Y, X ) ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.21/1.61 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.21/1.61 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T )
% 1.21/1.61 ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 T, X ), Z ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T )
% 1.21/1.61 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.21/1.61 ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.21/1.61 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.21/1.61 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ), X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), 'c_Finite__Set_Osetsum'( Z, T, U, X
% 1.21/1.61 ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.21/1.61 , X ), Z, X, X, U ), T, U, X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), 'c_Finite__Set_Osetsum'( Z, T, U, X
% 1.21/1.61 ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.21/1.61 , X ), Z, X, X, U ), T, U, X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_RealVector_OscaleR__class_OscaleR'(
% 1.21/1.61 Y, X ), Z ), X ), T ), hAPP( 'c_RealVector_OscaleR__class_OscaleR'( Y, X
% 1.21/1.61 ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_RealVector_OscaleR__class_OscaleR'(
% 1.21/1.61 Y, X ), Z ), X ), T ), hAPP( 'c_RealVector_OscaleR__class_OscaleR'( Y, X
% 1.21/1.61 ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Z, X ), T ) ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Z, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Z, X ), T ) ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Z, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_RealVector_OscaleR__class_OscaleR'(
% 1.21/1.61 Y, X ), Z ), X ), T ), hAPP( 'c_RealVector_OscaleR__class_OscaleR'( Y, X
% 1.21/1.61 ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Z, X ), T ) ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Z, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.21/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.21/1.61 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ), T, X ) ) ],
% 1.21/1.61 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.21/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.21/1.61 ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.21/1.61 Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', Y ) ) ) ) ],
% 1.21/1.61 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), Z ), T, X ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.21/1.61 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.21/1.61 X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ), W, X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ), W, X ) ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ), W, X ), X ), U ) ) ) ],
% 1.21/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.61 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.21/1.61 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.21/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~(
% 1.21/1.61 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.61 X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), Y ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( T, U, W, V0, V1, V2, V3, V4 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.21/1.61 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X,
% 1.21/1.61 X ), U, Z, X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.21/1.61 'c_Finite__Set_Osetsum'( Y, U, Z, X ) ), 'c_Finite__Set_Osetsum'( T, U, Z
% 1.21/1.61 , X ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.21/1.61 Y ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) )
% 1.21/1.61 ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.61 ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.21/1.61 , Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), Y )
% 1.21/1.61 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.21/1.61 , Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.21/1.61 Y ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) )
% 1.21/1.61 ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.61 ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.21/1.61 , Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), Y )
% 1.21/1.61 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.21/1.61 , Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( U, X ), Z ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ), X ), Z ) ), T ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( Y, Z, T, U, W, V0, V1, V2 ) ), =(
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), V3 ), V4 ) ), V4 ), V3 ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( Y, Z, T, U, W, V0, V1, V2 ) ), =(
% 1.21/1.61 V3, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), V3 ), V4 ) ), V4 ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.21/1.61 'class_RealVector_Oreal__normed__vector'( Y ) ), ~(
% 1.21/1.61 'class_RealVector_Oreal__normed__vector'( Z ) ), =( hAPP( hAPP( T, hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( Z ), U ), W ) ), V0 ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( Y ), hAPP( hAPP( T, U ), V0 ) ), hAPP( hAPP(
% 1.21/1.61 T, W ), V0 ) ) ), ~( 'c_RealVector_Obounded__bilinear'( T, Z, X, Y ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.21/1.61 'class_RealVector_Oreal__normed__vector'( Y ) ), ~(
% 1.21/1.61 'class_RealVector_Oreal__normed__vector'( Z ) ), =( hAPP( hAPP( T, U ),
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), W ), V0 ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( Y ), hAPP( hAPP( T, U ), W ) ), hAPP( hAPP(
% 1.21/1.61 T, U ), V0 ) ) ), ~( 'c_RealVector_Obounded__bilinear'( T, Z, X, Y ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( U, X ), Z ) ), W ) ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ), X ), Z ) ), T ), W ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.61 ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( U, X ), Z ) ), W ) ) ), =( T, hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ), X ), Z ) ), W ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), Y ), T ) ), Z ) ), ~( 'c_Ring__and__Field_Opordered__ring'( U, W, V0
% 1.21/1.61 , V1, V2, V3, V4, V5 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =( hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Z, X ), T ) ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Z, X ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =( hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Z, X ), T ) ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Z, X ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =( hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Z, X ), T ) ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Z, X ), hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.61 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.21/1.61 ) ],
% 1.21/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.61 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.21/1.61 ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), Y ), T ) ), Z ) ), ~( 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2,
% 1.21/1.61 V3 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.61 ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( U, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), U ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.21/1.61 Z, X ) ), 'c_HOL_Oinverse__class_Odivide'( Y, hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ), =( Z,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.21/1.61 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.21/1.61 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.61 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Osemigroup__mult'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.61 , Z ), X ), T ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( U, W, V0, V1, V2, V3, V4 ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Z, X ), T ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( U, W, V0, V1, V2, V3, V4 ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), Y ), T ) ), Z ) ), ~( 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2
% 1.21/1.61 , V3, V4, V5, V6 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.21/1.61 ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), Y ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), Y ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.61 ), Y ) ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.21/1.61 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.21/1.61 , W ) ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) )
% 1.21/1.61 ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.21/1.61 , X ), Y ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 Y, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Y ) )
% 1.21/1.61 ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.21/1.61 , X ), Y ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.21/1.61 , X ), Z ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.21/1.61 , X ), Y ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.61 Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) )
% 1.21/1.61 ) ],
% 1.21/1.61 [ ~( hBOOL( hAPP( X, 'c_Option_Ooption_Ooption__case'( Y, Z,
% 1.21/1.61 'c_Option_Ooption_ONone'( 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X,
% 1.21/1.61 Y ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ) ) ],
% 1.21/1.61 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', X ), Y
% 1.21/1.61 , 'tc_nat' ), 'c_SetInterval_Oord__class_OgreaterThanLessThan'( X, Y,
% 1.21/1.61 'tc_nat' ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.21/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T )
% 1.21/1.61 ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.21/1.61 ), Z ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( Y, Z, T, U, W, V0, V1, V2, V3 ) ), =( V4,
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), V4 ), V5 ) ), V5 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( Y, Z, T, U, W, V0, V1, V2, V3 ) ), =( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), V4 ), V5 ) ), V5 ), V4 ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), Y ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( T, U, W, V0, V1, V2, V3, V4, V5 ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.21/1.61 X ), T ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( T,
% 1.21/1.61 X ), Y ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ),
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( T, X ), Y ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ),
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( T, X ), Z ), X ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( T, X ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Ofield'( Y ) ), ~( =( hAPP( hAPP( Z, T ), U ),
% 1.21/1.61 hAPP( hAPP( Z, W ), U ) ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.21/1.61 'c_RealVector_Ovector__space'( Z, Y, X ) ), =( T, W ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Ofield'( Y ) ), ~( =( hAPP( hAPP( Z, T ), U ),
% 1.21/1.61 hAPP( hAPP( Z, W ), U ) ) ), ~( 'c_RealVector_Ovector__space'( Z, Y, X )
% 1.21/1.61 ), =( U, 'c_HOL_Ozero__class_Ozero'( X ) ), =( T, W ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Ofield'( Y ) ), ~( =( hAPP( hAPP( Z, T ), U ),
% 1.21/1.61 hAPP( hAPP( Z, T ), W ) ) ), =( T, 'c_HOL_Ozero__class_Ozero'( Y ) ), ~(
% 1.21/1.61 'c_RealVector_Ovector__space'( Z, Y, X ) ), =( U, W ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Ofield'( Y ) ), ~( =( hAPP( hAPP( Z, T ), U ),
% 1.21/1.61 hAPP( hAPP( Z, T ), W ) ) ), ~( 'c_RealVector_Ovector__space'( Z, Y, X )
% 1.21/1.61 ), =( T, 'c_HOL_Ozero__class_Ozero'( Y ) ), =( U, W ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Ofield'( Y ) ), ~( =( hAPP( hAPP( Z, T ), U ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_RealVector_Ovector__space'( Z
% 1.21/1.61 , Y, X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X ) ), =( T,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( Y ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.21/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.21/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.61 ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.61 ), Y ), Z, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y
% 1.21/1.61 , X ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ), hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ), X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.21/1.61 ), Y ), T ), X ), U ) ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ),
% 1.21/1.61 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =( hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =( hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.21/1.61 'c_SetInterval_Oord__class_OlessThan'( Y, X ),
% 1.21/1.61 'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ), =( Y, Z ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.61 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.61 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.21/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.61 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.61 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), Y ), Z ) ), T ) ), ~( 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2
% 1.21/1.61 , V3, V4, V5, V6 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.21/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), ~(
% 1.21/1.61 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.21/1.61 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.61 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.61 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ) ) ), =( Y, Z ) ],
% 1.21/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.61 X ) ) ), =( Y, Z ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.21/1.61 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Z, X ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Y ) ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.21/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.61 Y, X ), Y ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), Z ) ), X ),
% 1.21/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y
% 1.21/1.61 , X ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y
% 1.21/1.61 , X ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.21/1.61 ), Y ), Z ), X ), T ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.21/1.61 ), Y ), Z ), X ), T ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.21/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ), hAPP(
% 1.21/1.61 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.21/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.21/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.21/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.21/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.21/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.61 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =( hAPP(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), 'c_Finite__Set_Osetsum'( Z
% 1.21/1.61 , T, U, X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'(
% 1.21/1.61 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), Z, X, X, U ), T, U, X ) )
% 1.21/1.61 ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.21/1.61 , Y ) ), =( hAPP( 'c_Suc', X ), Y ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.21/1.61 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ),
% 1.21/1.61 hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ],
% 1.21/1.61 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.21/1.61 'c_lessequals'( hAPP( 'c_Suc', Y ), 'tc_nat' ), X ) ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.21/1.61 hAPP( hAPP( X, Z ), T ) ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( U, W, V0, X, V1, V2, V3 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( T, U, W, X, V0, V1, V2 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.21/1.61 hAPP( hAPP( X, Y ), T ) ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( U, W, V0, X, V1, V2, V3 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( Z, T ) ), hAPP( hAPP( U, Y ), T ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( U, Z, W, X, V0, V1, V2 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), T ), hAPP( hAPP( U, T ), Z ) ), ~(
% 1.21/1.61 'c_OrderedGroup_Opordered__ab__group__add'( U, Y, W, X, V0, V1, V2 ) ) ]
% 1.21/1.61 ,
% 1.21/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.21/1.61 hAPP( X, Y ), T ) ), U ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'(
% 1.21/1.61 Z, W, V0, X, V1, V2, V3 ) ) ],
% 1.21/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.62 hAPP( X, Z ), U ) ), T ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'(
% 1.21/1.62 Y, W, V0, X, V1, V2, V3 ) ) ],
% 1.21/1.62 [ ~( 'c_OrderedGroup_Opordered__ab__group__add'( X, Y, Z, T, U, W, V0 )
% 1.21/1.62 ), =( V1, hAPP( hAPP( T, hAPP( hAPP( X, V1 ), V2 ) ), V2 ) ) ],
% 1.21/1.62 [ ~( 'c_OrderedGroup_Opordered__ab__group__add'( X, Y, Z, T, U, W, V0 )
% 1.21/1.62 ), =( hAPP( hAPP( X, hAPP( hAPP( T, V1 ), V2 ) ), V2 ), V1 ) ],
% 1.21/1.62 [ ~( 'c_OrderedGroup_Opordered__ab__group__add'( X, Y, Z, T, U, W, V0 )
% 1.21/1.62 ), =( hAPP( hAPP( T, hAPP( hAPP( X, V1 ), V2 ) ), V2 ), V1 ) ],
% 1.21/1.62 [ ~( 'c_OrderedGroup_Opordered__ab__group__add'( X, Y, Z, T, U, W, V0 )
% 1.21/1.62 ), =( V1, hAPP( hAPP( X, hAPP( hAPP( T, V1 ), V2 ) ), V2 ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.21/1.62 hAPP( hAPP( U, Z ), T ) ) ), ~(
% 1.21/1.62 'c_OrderedGroup_Opordered__ab__group__add'( X, W, V0, U, V1, V2, V3 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.21/1.62 hAPP( U, Y ), T ) ), Z ) ), ~( 'c_OrderedGroup_Opordered__ab__group__add'(
% 1.21/1.62 X, W, V0, U, V1, V2, V3 ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.62 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( W, V0, V1, V2, X, Y, V3, V4 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.21/1.62 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( W, V0, V1, V2, X, Z, V3, V4 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.21/1.62 hAPP( U, Y ), T ) ), Z ) ), ~( 'c_Ring__and__Field_Opordered__ring'( U, W
% 1.21/1.62 , V0, V1, V2, X, V3, V4 ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.21/1.62 hAPP( hAPP( U, Z ), T ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( U,
% 1.21/1.62 W, V0, V1, V2, X, V3, V4 ) ) ],
% 1.21/1.62 [ ~( 'c_Ring__and__Field_Opordered__ring'( X, Y, Z, T, U, W, V0, V1 ) )
% 1.21/1.62 , =( V2, hAPP( hAPP( W, hAPP( hAPP( X, V2 ), V3 ) ), V3 ) ) ],
% 1.21/1.62 [ ~( 'c_Ring__and__Field_Opordered__ring'( X, Y, Z, T, U, W, V0, V1 ) )
% 1.21/1.62 , =( hAPP( hAPP( X, hAPP( hAPP( W, V2 ), V3 ) ), V3 ), V2 ) ],
% 1.21/1.62 [ ~( 'c_Ring__and__Field_Opordered__ring'( X, Y, Z, T, U, W, V0, V1 ) )
% 1.21/1.62 , =( hAPP( hAPP( W, hAPP( hAPP( X, V2 ), V3 ) ), V3 ), V2 ) ],
% 1.21/1.62 [ ~( 'c_Ring__and__Field_Opordered__ring'( X, Y, Z, T, U, W, V0, V1 ) )
% 1.21/1.62 , =( V2, hAPP( hAPP( X, hAPP( hAPP( W, V2 ), V3 ) ), V3 ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.62 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Ring__and__Field_Opordered__ring'( X, W
% 1.21/1.62 , V0, V1, V2, Y, V3, V4 ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.21/1.62 hAPP( X, Y ), T ) ), U ) ), ~( 'c_Ring__and__Field_Opordered__ring'( X, W
% 1.21/1.62 , V0, V1, V2, Z, V3, V4 ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), T ), hAPP( hAPP( U, T ), Z ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( X, W, V0, V1, V2, U, Y, V3 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( Z, T ) ), hAPP( hAPP( U, Y ), T ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( X, W, V0, V1, V2, U, Z, V3 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.21/1.62 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( Z, W, V0, V1, X, V2, V3, V4 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.62 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( Y, W, V0, V1, X, V2, V3, V4 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.21/1.62 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( U,
% 1.21/1.62 W, V0, V1, X, V2, V3, V4 ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.21/1.62 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( X,
% 1.21/1.62 U, W, V0, V1, V2, V3, V4 ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( X, T, U, W, V0, V1, V2, V3 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.21/1.62 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Ring__and__Field_Opordered__ring'( X,
% 1.21/1.62 U, W, V0, V1, V2, V3, V4 ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Y ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Z ) ), =( hAPP( hAPP( T,
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( Y ) ), U ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.21/1.62 , ~( 'c_RealVector_Obounded__bilinear'( T, Y, Z, X ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Y ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Z ) ), =( hAPP( hAPP( T, hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( Z ), U ) ), W ), hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( Y ), hAPP( hAPP( T, U ), W ) ) ), ~(
% 1.21/1.62 'c_RealVector_Obounded__bilinear'( T, Z, X, Y ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Y ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Z ) ), =( hAPP( hAPP( T, U ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.21/1.62 'c_RealVector_Obounded__bilinear'( T, Y, Z, X ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Y ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Z ) ), =( hAPP( hAPP( T, U ),
% 1.21/1.62 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), W ) ), hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( Y ), hAPP( hAPP( T, U ), W ) ) ), ~(
% 1.21/1.62 'c_RealVector_Obounded__bilinear'( T, Z, X, Y ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.21/1.62 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.21/1.62 T ), Z, X ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.62 , Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), X
% 1.21/1.62 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z
% 1.21/1.62 ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.62 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z
% 1.21/1.62 ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.62 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z
% 1.21/1.62 ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.62 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z
% 1.21/1.62 , X ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.21/1.62 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y
% 1.21/1.62 , X ), T ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.21/1.62 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y
% 1.21/1.62 , X ), T ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.21/1.62 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), T ), X ), Z ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z
% 1.21/1.62 ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), Z ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X
% 1.21/1.62 ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), T ), Z ) ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.21/1.62 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.21/1.62 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ), X ), Z ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.62 [ =( hAPP( X, hAPP( Y, Z ) ), hAPP( 'c_Fun_Ocomp'( X, Y, T, U, W ), Z )
% 1.21/1.62 ) ],
% 1.21/1.62 [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) )
% 1.21/1.62 ) ],
% 1.21/1.62 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.21/1.62 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.21/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), X ), T ) ), U ), X ), W ) )
% 1.21/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), T ) ), U ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ), W ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.21/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ), T ), X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( U, X
% 1.21/1.62 ), Z ) ), W ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ), X ), Z ) ), T ), X ),
% 1.21/1.62 W ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), hAPP( 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ), X ), U ) ), W ) ) ), ~(
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X
% 1.21/1.62 ), U ) ), Y ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Z, X ), U ) ), W ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.21/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ), T ), X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( U, X
% 1.21/1.62 ), Z ) ), W ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.21/1.62 ), U ), Y ), X ), Z ) ), W ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ),
% 1.21/1.62 Y, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Ofield'( Y ) ), =( hAPP( hAPP( Z, T ), hAPP( hAPP(
% 1.21/1.62 Z, U ), W ) ), hAPP( hAPP( Z, U ), hAPP( hAPP( Z, T ), W ) ) ), ~(
% 1.21/1.62 'c_RealVector_Ovector__space'( Z, Y, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.62 ) ) ), =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.62 ) ) ), =( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.62 'class_OrderedGroup_Oab__group__add'( Y ) ), =( hAPP( Z,
% 1.21/1.62 'c_Finite__Set_Osetsum'( T, U, W, Y ) ), 'c_Finite__Set_Osetsum'(
% 1.21/1.62 'c_COMBB'( Z, T, Y, X, W ), U, W, X ) ), ~( 'c_RealVector_Oadditive'( Z,
% 1.21/1.62 Y, X ) ) ],
% 1.21/1.62 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.21/1.62 hAPP( 'c_Suc', Y ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.21/1.62 'tc_nat' ), Y ) ) ],
% 1.21/1.62 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ),
% 1.21/1.62 hAPP( 'c_Suc', X ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.21/1.62 'tc_nat' ), X ) ) ],
% 1.21/1.62 [ =( X, Y ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y )
% 1.21/1.62 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP(
% 1.21/1.62 'c_Suc', Y ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.21/1.62 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Otimes__class_Otimes'( U, X )
% 1.21/1.62 , Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( W, X ), T ), Z, X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.21/1.62 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), U ) ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Z, X ), U ), X ) ), =( U,
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.21/1.62 ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.21/1.62 , X ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.21/1.62 , X ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.21/1.62 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.21/1.62 , X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.62 ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) )
% 1.21/1.62 , ~( 'c_OrderedGroup_Opordered__ab__group__add'( T, U, W, V0, V1, V2, V3
% 1.21/1.62 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), ~(
% 1.21/1.62 'c_OrderedGroup_Opordered__ab__group__add'( T, U, W, V0, V1, V2, V3 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.21/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.62 X ), X ), Y ) ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.21/1.62 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_OrderedGroup_Osemigroup__add'( X, U )
% 1.21/1.62 ) ],
% 1.21/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.21/1.62 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.21/1.62 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), W ), T ), Z, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.21/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.62 Y, X ), Z ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.21/1.62 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ), X ), Z ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.21/1.62 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X
% 1.21/1.62 ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), T ), Z ) ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z
% 1.21/1.62 ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), Z ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.21/1.62 ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.21/1.62 , X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) )
% 1.21/1.62 ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.21/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ), hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( Y, X ), Z ) ) ],
% 1.21/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( U, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), U ) ) )
% 1.21/1.62 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.21/1.62 , Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.21/1.62 , Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Y ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Z ) ), =( hAPP( hAPP( T, hAPP(
% 1.21/1.62 'c_RealVector_OscaleR__class_OscaleR'( U, Z ), W ) ), V0 ), hAPP(
% 1.21/1.62 'c_RealVector_OscaleR__class_OscaleR'( U, Y ), hAPP( hAPP( T, W ), V0 ) )
% 1.21/1.62 ), ~( 'c_RealVector_Obounded__bilinear'( T, Z, X, Y ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Y ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Z ) ), =( hAPP( hAPP( T, U ),
% 1.21/1.62 hAPP( 'c_RealVector_OscaleR__class_OscaleR'( W, X ), V0 ) ), hAPP(
% 1.21/1.62 'c_RealVector_OscaleR__class_OscaleR'( W, Y ), hAPP( hAPP( T, U ), V0 ) )
% 1.21/1.62 ), ~( 'c_RealVector_Obounded__bilinear'( T, Z, X, Y ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.62 , Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.21/1.62 , X ) ), T, X ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.62 , Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), X
% 1.21/1.62 ), Z ), T, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Oring'( Y, Z, T, U, W, V0 ) ), =( V1, hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), V1 ), V2 ) ), V2 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Oring'( Y, Z, T, U, W, V0 ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), V1 ), V2 ) ), V2 ), V1 ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.62 Y, X ), Y ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), Z ) ) ) ), =(
% 1.21/1.62 Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.62 Y, X ), Y ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), Z ) ) ) ), =(
% 1.21/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y
% 1.21/1.62 , X ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.21/1.62 ), Y ), Z ), X ), T ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.21/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.21/1.62 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.21/1.62 [ ~( =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( X,
% 1.21/1.62 hAPP( hAPP( Y, W ), T ) ), V0 ) ) ), ~( 'c_Ring__and__Field_Oring'( V1,
% 1.21/1.62 V2, V3, X, Y, V4 ) ), =( U, hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP( V1
% 1.21/1.62 , W ), Z ) ), T ) ), V0 ) ) ],
% 1.21/1.62 [ ~( =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( X,
% 1.21/1.62 hAPP( hAPP( Y, W ), T ) ), V0 ) ) ), ~( 'c_Ring__and__Field_Oring'( V1,
% 1.21/1.62 V2, V3, X, Y, V4 ) ), =( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP( V1, Z
% 1.21/1.62 ), W ) ), T ) ), U ), V0 ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X
% 1.21/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.62 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.62 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.62 [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, 't_a', Z, T ), 'v_x' ), hAPP( Y, hAPP(
% 1.21/1.62 X, 'v_x' ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( Y, Z, T, U, W, V0, V1, V2, V3 ) ), =( hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), V4 ), V5 ) ), V5 ), V4 ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( Y, Z, T, U, W, V0, V1, V2, V3 ) ), =( V4,
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), V4 ), V5 ) ), V5 ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), Z ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ), X ),
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), Z ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ), X ),
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.21/1.62 'c_Suc', X ) ) ) ],
% 1.21/1.62 [ ~( =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, T ), U ) ) ), =( Z, W )
% 1.21/1.62 , =( U, W ), ~( 'c_Ring__and__Field_Ofield'( V0, V1, V2, X, V3, V4, W, V5
% 1.21/1.62 , V6 ) ), =( hAPP( hAPP( V1, Y ), U ), hAPP( hAPP( V1, T ), Z ) ) ],
% 1.21/1.62 [ ~( =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, T ), U ) ) ), =( U, W )
% 1.21/1.62 , =( Z, W ), ~( 'c_Ring__and__Field_Ofield'( V0, X, V1, V2, V3, V4, W, V5
% 1.21/1.62 , V6 ) ), =( hAPP( hAPP( V2, Y ), U ), hAPP( hAPP( V2, T ), Z ) ) ],
% 1.21/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.21/1.62 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.21/1.62 [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ), 'c_Finite__Set_Ofinite'(
% 1.21/1.62 Y, X ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.21/1.62 , X ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), T ), Z, X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.21/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z
% 1.21/1.62 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.62 ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z
% 1.21/1.62 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.21/1.62 ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), Z ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ), ~(
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.62 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) )
% 1.21/1.62 ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z
% 1.21/1.62 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.21/1.62 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z
% 1.21/1.62 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.62 ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z
% 1.21/1.62 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.21/1.62 ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), Z ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~(
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.62 X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) )
% 1.21/1.62 ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z
% 1.21/1.62 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.21/1.62 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z
% 1.21/1.62 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.21/1.62 ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Y
% 1.21/1.62 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T
% 1.21/1.62 ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z
% 1.21/1.62 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.62 ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z
% 1.21/1.62 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Y ) ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.21/1.62 ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ), Z, X ),
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ), T, X ),
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.21/1.62 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.21/1.62 Y, X, X, Z ), T, Z, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.21/1.62 'c_Finite__Set_Osetsum'( Y, T, Z, X ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.21/1.62 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ), X ), Z )
% 1.21/1.62 ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.21/1.62 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.62 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T )
% 1.21/1.62 ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.62 T, X ), Z ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T )
% 1.21/1.62 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.62 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.21/1.62 X ), Y ) ), Y ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.21/1.62 X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.21/1.62 X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.21/1.62 X ), Y ) ), Y ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.21/1.62 X ), Y ) ), Y ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.21/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ) ), T ) ), ~( 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2,
% 1.21/1.62 V3 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( T, U, W, V0, V1, V2, V3, V4 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.62 ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) )
% 1.21/1.62 , ~( 'c_Ring__and__Field_Opordered__ring'( T, U, W, V0, V1, V2, V3, V4 )
% 1.21/1.62 ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.21/1.62 , hAPP( 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.21/1.62 'tc_nat' ), Y ) ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.21/1.62 'c_Suc', Y ) ) ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.21/1.62 , hAPP( 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.21/1.62 'tc_nat' ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.21/1.62 , X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.21/1.62 , X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.21/1.62 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.21/1.62 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), Z )
% 1.21/1.62 ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.21/1.62 X ), Z ), X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), Z )
% 1.21/1.62 ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.21/1.62 X ), Z ), X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) )
% 1.21/1.62 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) )
% 1.21/1.62 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.62 ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.62 ), Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.21/1.62 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, X ), T ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Z ), U ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.21/1.62 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.21/1.62 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.21/1.62 ), T ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) )
% 1.21/1.62 ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.21/1.62 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.21/1.62 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T
% 1.21/1.62 ), Y ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) )
% 1.21/1.62 ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.62 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.62 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Oring'( T, U, W, V0, V1, V2 ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.21/1.62 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), U ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ), =( Z, U
% 1.21/1.62 ), =( Y, T ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.21/1.62 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), U ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ) ), =( Z, U
% 1.21/1.62 ), =( Y, T ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( T, U, W, V0, V1, V2, V3, V4, V5 ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.21/1.62 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.21/1.62 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~(
% 1.21/1.62 hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), ~(
% 1.21/1.62 'c_OrderedGroup_Opordered__ab__group__add'( T, U, W, V0, V1, V2, V3 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), T ), X ), Z ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), Z ), X ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), Z ), X ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), Z ), X ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.62 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.21/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.62 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.21/1.62 ), T ), X ), Z ) ) ), ~( 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2,
% 1.21/1.62 V3, V4, V5, V6 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.21/1.62 ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), T ), Z ) ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.21/1.62 , Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X )
% 1.21/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ), X ), Z ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), Z ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ) ), ~(
% 1.21/1.62 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.21/1.62 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.62 X ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), U )
% 1.21/1.62 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), Z ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ) ), ~(
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.21/1.62 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.62 X ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~(
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Ocomp'( Y, Z, T, U, W ), U, V0, W ),
% 1.21/1.62 'c_Fun_Ocomp'( 'c_Fun_Ocomp'( X, Y, U, V0, T ), Z, T, V0, W ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.21/1.62 Y ), X ), Z ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Ofield'( Y ) ), =( hAPP( hAPP( Z, T ), hAPP( hAPP(
% 1.21/1.62 Z, U ), W ) ), hAPP( hAPP( Z, hAPP( 'c_HOL_Otimes__class_Otimes'( T, Y )
% 1.21/1.62 , U ) ), W ) ), ~( 'c_RealVector_Ovector__space'( Z, Y, X ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( 'c_Suc', Y ) ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), Z ), X ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.62 Z, X ), T ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_OrderedGroup_Osemigroup__mult'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.62 , Z ), X ), T ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( U, W, V0, V1, V2, V3, V4, V5 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), X ) )
% 1.21/1.62 ) ],
% 1.21/1.62 [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, 't_a' ), 'v_x' ), hAPP( X, hAPP( Y
% 1.21/1.62 , 'v_x' ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Ofield'( Y ) ), =( hAPP( hAPP( Z, hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( Y ), T ), U ) ), W ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( Z, T ), W ) ), hAPP( hAPP(
% 1.21/1.62 Z, U ), W ) ) ), ~( 'c_RealVector_Ovector__space'( Z, Y, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Ofield'( Y ) ), =( hAPP( hAPP( Z, T ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), U ), W ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP(
% 1.21/1.62 Z, T ), W ) ) ), ~( 'c_RealVector_Ovector__space'( Z, Y, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y
% 1.21/1.62 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X
% 1.21/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.62 Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.21/1.62 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), X ), T )
% 1.21/1.62 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X
% 1.21/1.62 ), X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ), X ), Y ) ) ), hBOOL(
% 1.21/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z
% 1.21/1.62 ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) )
% 1.21/1.62 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.21/1.62 Y, T, X ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.21/1.62 , X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.21/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.62 X ), X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.62 X ), X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.21/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.21/1.62 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.21/1.62 , X ), Y ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.21/1.62 ), Y ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X
% 1.21/1.62 , 'tc_nat' ), Z ) ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.62 T, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) )
% 1.21/1.62 ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.21/1.62 , X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.21/1.62 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.21/1.62 Y, X ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) )
% 1.21/1.62 ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.21/1.62 ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, Y ), Y ), Z ), =( Y, T ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( U, X, Z, W, V0, V1, T, V2, V3 ) ) ],
% 1.21/1.62 [ =( X, Y ), ~( 'c_Ring__and__Field_Ofield'( Z, T, U, W, V0, V1, Y, V2,
% 1.21/1.62 V3 ) ), =( hAPP( hAPP( T, hAPP( hAPP( W, V4 ), X ) ), X ), V4 ) ],
% 1.21/1.62 [ =( X, Y ), ~( 'c_Ring__and__Field_Ofield'( Z, T, U, W, V0, V1, Y, V2,
% 1.21/1.62 V3 ) ), =( V4, hAPP( hAPP( T, hAPP( hAPP( W, V4 ), X ) ), X ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), Z ), T ), =( Z, U ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( Y, W, T, X, V0, V1, U, V2, V3 ) ) ],
% 1.21/1.62 [ =( X, Y ), ~( 'c_Ring__and__Field_Ofield'( Z, T, hAPP( hAPP( T, U ), X
% 1.21/1.62 ), W, V0, V1, Y, V2, V3 ) ), =( U, X ) ],
% 1.21/1.62 [ =( X, Y ), ~( 'c_Ring__and__Field_Ofield'( Z, T, U, W, V0, V1, Y, V2,
% 1.21/1.62 V3 ) ), =( hAPP( hAPP( T, X ), X ), U ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.21/1.62 hAPP( X, hAPP( hAPP( W, U ), Y ) ), T ) ), U ) ), =( U, V0 ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( V1, Z, V2, W, V3, V4, V0, X, V5 ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.62 hAPP( X, Z ), hAPP( hAPP( W, T ), U ) ) ), T ) ), =( T, V0 ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( V1, Y, V2, W, V3, V4, V0, X, V5 ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.21/1.62 hAPP( X, hAPP( hAPP( W, U ), Y ) ), T ) ), U ) ), =( U, V0 ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( V1, Z, V2, W, X, V3, V0, V4, V5 ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.21/1.62 hAPP( X, Z ), hAPP( hAPP( W, T ), U ) ) ), T ) ), =( T, V0 ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( V1, Y, V2, W, X, V3, V0, V4, V5 ) ) ],
% 1.21/1.62 [ =( X, Y ), ~( 'c_Ring__and__Field_Ofield'( Z, T, U, W, V0, V1, Y, V2,
% 1.21/1.62 V3 ) ), =( V4, hAPP( hAPP( W, hAPP( hAPP( T, V4 ), X ) ), X ) ) ],
% 1.21/1.62 [ =( X, Y ), ~( 'c_Ring__and__Field_Ofield'( Z, T, U, W, V0, V1, Y, V2,
% 1.21/1.62 V3 ) ), =( hAPP( hAPP( W, hAPP( hAPP( T, V4 ), X ) ), X ), V4 ) ],
% 1.21/1.62 [ =( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), =( Y, U ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( X, Z, T, W, V0, V1, U, V2, V3 ) ) ],
% 1.21/1.62 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), hAPP( X, T
% 1.21/1.62 ) ) ), =( T, U ), ~( 'c_Ring__and__Field_Ofield'( W, Y, V0, V1, V2, X, U
% 1.21/1.62 , V3, V4 ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, T ) ), hAPP( hAPP( X, Z ),
% 1.21/1.62 T ) ), =( T, U ), ~( 'c_Ring__and__Field_Ofield'( W, X, V0, V1, V2, Y, U
% 1.21/1.62 , V3, V4 ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), T ), =( Z, U ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( W, X, V0, Y, V1, V2, U, V3, V4 ) ) ],
% 1.21/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), Z ), =( T, U ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( W, X, V0, Y, V1, V2, U, V3, V4 ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.21/1.62 'c_SetInterval_Oord__class_OatMost'( Y, X ),
% 1.21/1.62 'c_SetInterval_Oord__class_OatMost'( Z, X ) ) ), =( Y, Z ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.62 , Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.62 , Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.62 'class_OrderedGroup_Oab__group__add'( Y ) ), =( hAPP( Z, hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), T ) ), hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( Y ), hAPP( Z, T ) ) ), ~(
% 1.21/1.62 'c_RealVector_Oadditive'( Z, X, Y ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.62 'class_OrderedGroup_Oab__group__add'( Y ) ), =( hAPP( Z,
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.21/1.62 'c_RealVector_Oadditive'( Z, Y, X ) ) ],
% 1.21/1.62 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.21/1.62 hAPP( 'c_Suc', Y ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ),
% 1.21/1.62 X ) ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =( hAPP(
% 1.21/1.62 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.21/1.62 X ) ), hAPP( 'c_RealVector_OscaleR__class_OscaleR'( Z, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__vector'( X ) ), ~( =( hAPP(
% 1.21/1.62 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), Z ), hAPP(
% 1.21/1.62 'c_RealVector_OscaleR__class_OscaleR'( T, X ), Z ) ) ), =( Z,
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, T ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.21/1.62 , hAPP( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.21/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.21/1.62 ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( T, X ), Z ), X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( T, X ), Y ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z
% 1.21/1.62 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Z, X ), T ), X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.62 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Otimes__class_Otimes'( Z, X ), Y
% 1.21/1.62 ), X ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Y ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.62 ), X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.21/1.62 ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.21/1.62 ), =( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), U ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( T, X ), U ) ) ), =( Z,
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.21/1.62 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.62 , Z ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ), X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.21/1.62 , X ) ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X )
% 1.21/1.62 , Z ), hAPP( 'c_HOL_Otimes__class_Otimes'( T, X ), Z ), X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), X
% 1.21/1.62 ), Z ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ), X ), Z ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.21/1.62 , Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X )
% 1.21/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.21/1.62 ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), T ), Z ) ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.21/1.62 ), T ), X ), Z ) ) ), ~( 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2,
% 1.21/1.62 V3 ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.21/1.62 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.21/1.62 X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.21/1.62 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) )
% 1.21/1.62 ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP( 'c_Suc', Y ) ) ) )
% 1.21/1.62 ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ), Y, X ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ =( 'c_Fun_Ofcomp'( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W, Z, U, V0 ),
% 1.21/1.62 'c_Fun_Ofcomp'( X, 'c_Fun_Ofcomp'( Y, W, T, U, V0 ), Z, T, V0 ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.21/1.62 , X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z, X ), Y ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( Y, 'tc_nat' ), X ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), Z ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), Z ), X ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Z, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), T ), Z, X ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), Z ), T, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.21/1.62 ), Y ) ), Z ) ), Z ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~(
% 1.21/1.62 'c_OrderedGroup_Opordered__ab__group__add'( U, W, V0, V1, V2, V3, V4 ) )
% 1.21/1.62 ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~(
% 1.21/1.62 'c_OrderedGroup_Opordered__ab__group__add'( U, W, V0, V1, V2, V3, V4 ) )
% 1.21/1.62 ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ),
% 1.21/1.62 'c_OrderedGroup_Osemigroup__add'( 'c_HOL_Oplus__class_Oplus'( X ), X ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.21/1.62 , hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.21/1.62 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z )
% 1.21/1.62 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.21/1.62 , hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X
% 1.21/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.21/1.62 , hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.21/1.62 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T )
% 1.21/1.62 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.21/1.62 , hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.21/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), X
% 1.21/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.21/1.62 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~(
% 1.21/1.62 hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.21/1.62 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~(
% 1.21/1.62 hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Opordered__ring'( T, U, W, V0, V1, V2, V3, V4 ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Ofield'( Y ) ), =( hAPP( hAPP( Z, T ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), U ), W ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z
% 1.21/1.62 , T ), W ) ) ), ~( 'c_RealVector_Ovector__space'( Z, Y, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.62 'class_Ring__and__Field_Ofield'( Y ) ), =( hAPP( hAPP( Z, hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( Y ), T ), U ) ), W ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( Z, T ), W ) ), hAPP( hAPP( Z
% 1.21/1.62 , U ), W ) ) ), ~( 'c_RealVector_Ovector__space'( Z, Y, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.21/1.62 ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.21/1.62 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.21/1.62 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Oring'( U, W, V0, V1, V2, V3 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~(
% 1.21/1.62 'class_OrderedGroup_Oab__group__add'( Y ) ), =( hAPP( Z, hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( Y ), hAPP( Z, T ) ), hAPP( Z, U ) ) ), ~(
% 1.21/1.62 'c_RealVector_Oadditive'( Z, X, Y ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.21/1.62 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), T ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.21/1.62 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( Y, X ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), T ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X ), Z ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.21/1.62 X ), Y ), Z ) ), Z ), Y ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.21/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.21/1.62 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.21/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.21/1.62 , X ) ), T, X ) ) ],
% 1.21/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.21/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.21/1.62 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.21/1.62 ), Z ), T, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~(
% 1.21/1.62 'c_Ring__and__Field_Ofield'( U, W, V0, V1, V2, V3, V4, V5, V6 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ),
% 1.21/1.62 'c_OrderedGroup_Ocancel__ab__semigroup__add__axioms'(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( Y, X
% 1.21/1.62 ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_HOL_Otimes__class_Otimes'( T, X ), Z ) ), U ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Otimes__class_Otimes'( hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), Z ) ), U ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.21/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =( hAPP(
% 1.21/1.62 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), Z ) ), hAPP(
% 1.21/1.62 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =( hAPP(
% 1.21/1.62 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), Z ) ), hAPP(
% 1.21/1.62 'c_RealVector_OscaleR__class_OscaleR'( Y, X ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y, hAPP(
% 1.21/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), T ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.21/1.62 Y ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.21/1.62 Y ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.21/1.62 Y ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.21/1.62 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.21/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.21/1.62 Y ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.21/1.62 Y ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.21/1.62 Y ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.21/1.62 Y ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ) ), Z ), Y ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Y ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Z ) ), =( hAPP( hAPP( T, U ),
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), W ), V0 ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( Y ), hAPP( hAPP( T, U ), W ) ), hAPP( hAPP( T
% 1.21/1.62 , U ), V0 ) ) ), ~( 'c_RealVector_Obounded__bilinear'( T, Z, X, Y ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Y ) ), ~(
% 1.21/1.62 'class_RealVector_Oreal__normed__vector'( Z ) ), =( hAPP( hAPP( T, hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( Z ), U ), W ) ), V0 ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( Y ), hAPP( hAPP( T, U ), V0 ) ), hAPP( hAPP(
% 1.21/1.62 T, W ), V0 ) ) ), ~( 'c_RealVector_Obounded__bilinear'( T, Z, X, Y ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.21/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.21/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.21/1.62 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X, X ), U, Z, X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y, U, Z, X ) )
% 1.21/1.62 , 'c_Finite__Set_Osetsum'( T, U, Z, X ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.21/1.62 'c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1'( Z, Y, T, U, X )
% 1.21/1.62 ), hAPP( T, 'c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1'( Z,
% 1.21/1.62 Y, T, U, X ) ) ) ), =( 'c_Finite__Set_Osetsum'( Y, Z, U, X ),
% 1.21/1.62 'c_Finite__Set_Osetsum'( T, Z, U, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.21/1.62 'c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1'( Z, Y, T, U, X ) )
% 1.21/1.62 , hAPP( T, 'c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1'( Z, Y,
% 1.21/1.62 T, U, X ) ) ) ), =( 'c_Finite__Set_Osetsum'( Y, Z, U, X ),
% 1.21/1.62 'c_Finite__Set_Osetsum'( T, Z, U, X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.21/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OlessThan'( hAPP(
% 1.21/1.62 'c_Suc', Z ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.21/1.62 'c_SetInterval_Oord__class_OlessThan'( Z, 'tc_nat' ), 'tc_nat', X ) ),
% 1.21/1.62 hAPP( Y, Z ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.21/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatMost'( hAPP(
% 1.21/1.62 'c_Suc', Z ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.21/1.62 'c_SetInterval_Oord__class_OatMost'( Z, 'tc_nat' ), 'tc_nat', X ) ), hAPP(
% 1.21/1.62 Y, hAPP( 'c_Suc', Z ) ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( X, Y ) ),
% 1.21/1.62 'c_Finite__Set_Osetsum'( Z,
% 1.21/1.62 'c_SetInterval_Oord__class_OgreaterThanLessThan'( Y, T, 'tc_nat' ),
% 1.21/1.62 'tc_nat', 't_a' ) ), 'c_Finite__Set_Osetsum'( X,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, T, 'tc_nat' ), 'tc_nat'
% 1.21/1.62 , 't_a' ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.62 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__singleton__1'( X,
% 1.21/1.62 Z, Y, T ), 'tc_nat' ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.62 Y, 'tc_nat' ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( X, Y ) ),
% 1.21/1.62 'c_Finite__Set_Osetsum'( Z,
% 1.21/1.62 'c_SetInterval_Oord__class_OgreaterThanLessThan'( Y, T, 'tc_nat' ),
% 1.21/1.62 'tc_nat', 't_a' ) ), 'c_Finite__Set_Osetsum'( X,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, T, 'tc_nat' ), 'tc_nat'
% 1.21/1.62 , 't_a' ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ),
% 1.21/1.62 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__singleton__1'( X,
% 1.21/1.62 Z, Y, T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ),
% 1.21/1.62 T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), ~( =( hAPP( X,
% 1.21/1.62 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__singleton__1'( Y,
% 1.21/1.62 X, Z, T ) ), hAPP( Y,
% 1.21/1.62 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__singleton__1'( Y,
% 1.21/1.62 X, Z, T ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' )
% 1.21/1.62 , T ) ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( Y, Z
% 1.21/1.62 ) ), 'c_Finite__Set_Osetsum'( X,
% 1.21/1.62 'c_SetInterval_Oord__class_OgreaterThanLessThan'( Z, T, 'tc_nat' ),
% 1.21/1.62 'tc_nat', 't_a' ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.21/1.62 , 't_a' ) ) ],
% 1.21/1.62 [ ~( 'class_HOL_Oord'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.21/1.62 Y ) ), =( 'c_Finite__Set_Osetsum'( Z,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, X ), X, Y ),
% 1.21/1.62 'c_Finite__Set_Osetsum'( W, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.21/1.62 T, U, X ), X, Y ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.62 'c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1'( T, U, Z, W, X, Y )
% 1.21/1.62 , X ), U ) ) ],
% 1.21/1.62 [ ~( 'class_HOL_Oord'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.21/1.62 Y ) ), =( 'c_Finite__Set_Osetsum'( Z,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, X ), X, Y ),
% 1.21/1.62 'c_Finite__Set_Osetsum'( W, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.21/1.62 T, U, X ), X, Y ) ), hBOOL( hAPP( 'c_lessequals'( T, X ),
% 1.21/1.62 'c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1'( T, U, Z, W, X, Y )
% 1.21/1.62 ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.21/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.21/1.62 hAPP( 'c_Suc', Z ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.21/1.62 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.21/1.62 , X ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Ominus__class_Ominus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.21/1.62 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.21/1.62 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( U, T, 'tc_nat' ), 'tc_nat'
% 1.21/1.62 , X ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, 'tc_nat' ), T ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( Z, 'tc_nat' ), U ) ) ) ],
% 1.21/1.62 [ 'c_Finite__Set_Ofinite'( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.21/1.62 X, Y, 'tc_nat' ), 'tc_nat' ) ],
% 1.21/1.62 [ =( hAPP( 'c_Fun_Ofcomp'( 'v_f', 'v_g', 't_a', 't_b', 't_c' ), 'v_x' )
% 1.21/1.62 , hAPP( 'v_g', hAPP( 'v_f', 'v_x' ) ) ) ],
% 1.21/1.62 [ =( hAPP( 'c_Fun_Ocomp'( 'v_f', 'v_g', 't_a', 't_b', 't_c' ), 'v_x' ),
% 1.21/1.62 hAPP( 'v_f', hAPP( 'v_g', 'v_x' ) ) ) ],
% 1.21/1.62 [ =( 'c_Map_Omap__comp'( 'v_f', 'v_g', 'v_k', 't_a', 't_b', 't_c' ),
% 1.21/1.62 'c_Option_Ooption_Ooption__case'( 'c_Option_Ooption_ONone'( 't_b' ),
% 1.21/1.62 'v_f', hAPP( 'v_g', 'v_k' ), 'tc_Option_Ooption'( 't_b' ), 't_a' ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.21/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.21/1.62 Z, T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), T,
% 1.21/1.62 'tc_nat' ), 'tc_nat', X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.21/1.62 Z, 'tc_nat' ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.21/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.21/1.62 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.21/1.62 , X ) ), hAPP( Y, T ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T,
% 1.21/1.62 'tc_nat' ), Z ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'(
% 1.21/1.62 Y, 'c_SetInterval_Oord__class_OgreaterThanLessThan'( Z, T, 'tc_nat' ),
% 1.21/1.62 'tc_nat', X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.21/1.62 , X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), T ) )
% 1.21/1.62 ) ],
% 1.21/1.62 [ ~( 'class_HOL_Oord'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.21/1.62 Y ) ), ~( =( hAPP( Z,
% 1.21/1.62 'c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1'( T, U, Z, W, X, Y )
% 1.21/1.62 ), hAPP( W, 'c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1'( T, U,
% 1.21/1.62 Z, W, X, Y ) ) ) ), =( 'c_Finite__Set_Osetsum'( Z,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, X ), X, Y ),
% 1.21/1.62 'c_Finite__Set_Osetsum'( W, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.21/1.62 T, U, X ), X, Y ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'v_k', 'tc_nat' ), 'v_n' ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), =( hAPP( 'v_g'
% 1.21/1.62 , X ), hAPP( 'v_f', X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.21/1.62 'tc_nat' ), 'v_k' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'v_m', 'tc_nat'
% 1.21/1.62 ), X ) ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'v_m', 'tc_nat' ), 'v_k' ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.21/1.62 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, 'tc_nat' ), 'tc_nat'
% 1.21/1.62 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.21/1.62 , X ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), U ) ) ), ~( hBOOL(
% 1.21/1.62 hAPP( 'c_lessequals'( Z, 'tc_nat' ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), =( hAPP( 'v_h'
% 1.21/1.62 , X ), hAPP( 'v_f', X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.21/1.62 'tc_nat' ), 'v_n' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'v_k', 'tc_nat'
% 1.21/1.62 ), X ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.21/1.62 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.21/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ) ), T ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ) ), T ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.21/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.21/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.21/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.21/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), =( hAPP( 'v_h'
% 1.21/1.62 , X ), hAPP( 'v_f', X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.21/1.62 'tc_nat' ), 'v_n' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'v_k', 'tc_nat'
% 1.21/1.62 ), X ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), =( hAPP( 'v_g'
% 1.21/1.62 , X ), hAPP( 'v_f', X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.21/1.62 'tc_nat' ), 'v_k' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'v_m', 'tc_nat'
% 1.21/1.62 ), X ) ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'v_k', 'tc_nat' ), 'v_n' ) ) ],
% 1.21/1.62 [ hBOOL( hAPP( 'c_lessequals'( 'v_m', 'tc_nat' ), 'v_k' ) ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ],
% 1.21/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 't_a' ),
% 1.21/1.62 'c_Finite__Set_Osetsum'( 'v_g',
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'v_m', 'v_k', 'tc_nat' ),
% 1.21/1.62 'tc_nat', 't_a' ) ), 'c_Finite__Set_Osetsum'( 'v_h',
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'v_k', 'v_n', 'tc_nat' ),
% 1.21/1.62 'tc_nat', 't_a' ) ), 'c_Finite__Set_Osetsum'( 'v_f',
% 1.21/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'v_m', 'v_n', 'tc_nat' ),
% 1.21/1.62 'tc_nat', 't_a' ) ) ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.21/1.62 'class_OrderedGroup_Oab__semigroup__add'( X ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.21/1.62 'class_OrderedGroup_Osemigroup__add'( X ) ],
% 1.21/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.21/1.62 'class_OrderedGroup_Omonoid__add'( X ) ],
% 1.21/1.62 [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.21/1.62 'class_Lattices_Olattice'( Y ) ) ],
% 1.21/1.62 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.21/1.62 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.21/1.62 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_fun'( X, Y ) ), ~(
% 1.21/1.62 'class_Finite__Set_Ofinite_Ofinite'( Y ) ), ~(
% 1.21/1.62 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ],
% 1.21/1.62 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.21/1.62 'class_Orderings_Opreorder'( Y ) ) ],
% 1.21/1.62 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.21/1.62 'class_Lattices_Olattice'( Y ) ) ],
% 1.21/1.62 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.21/1.62 'class_Orderings_Oorder'( Y ) ) ],
% 1.21/1.62 [ 'class_HOL_Oord'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Oord'( Y ) ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.21/1.62 ],
% 1.21/1.62 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.21/1.62 ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.21/1.62 ],
% 1.21/1.62 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Osemigroup__mult'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_HOL_Oord'( 'tc_nat' ) ],
% 1.21/1.62 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 1.21/1.62 [ 'class_Lattices_Oboolean__algebra'( 'tc_bool' ) ],
% 1.21/1.62 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_bool' ) ],
% 1.21/1.62 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.21/1.62 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.21/1.62 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.21/1.62 [ 'class_HOL_Oord'( 'tc_bool' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.21/1.62 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.21/1.62 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.21/1.62 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.21/1.62 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Olordered__ab__group__add__join'(
% 1.21/1.62 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.21/1.62 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_RealDef_Oreal'
% 1.21/1.62 ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_RealDef_Oreal'
% 1.21/1.62 ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_RealDef_Oreal'
% 1.21/1.62 ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_RealDef_Oreal' )
% 1.21/1.62 ],
% 1.21/1.62 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_RealDef_Oreal' )
% 1.21/1.62 ],
% 1.21/1.62 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_RealDef_Oreal' ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_RealDef_Oreal' ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_RealDef_Oreal' ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_RealDef_Oreal' ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_RealDef_Oreal' ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_RealDef_Oreal' ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_RealDef_Oreal' ) ]
% 1.21/1.62 ,
% 1.21/1.62 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_RealVector_Oreal__normed__vector'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Oordered__field'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_RealVector_Oreal__normed__field'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Osemigroup__mult'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Lattices_Oupper__semilattice'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Oab__group__add'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Omult__zero'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Omult__mono'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Osemiring'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_RealVector_Oreal__algebra'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_RealVector_Oreal__vector'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_RealVector_Oreal__field'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Ofield'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Oring'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Lattices_Olattice'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_HOL_Oord'( 'tc_RealDef_Oreal' ) ],
% 1.21/1.62 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_Option_Ooption'( X ) ), ~(
% 1.21/1.62 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ],
% 1.21/1.62 [ 'c_fequal'( X, X, Y ) ],
% 1.21/1.62 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.21/1.62 ] .
% 1.21/1.62
% 1.21/1.62
% 1.21/1.62 percentage equality = 0.220309, percentage horn = 0.868020
% 1.21/1.62 This is a problem with some equality
% 1.21/1.62
% 1.21/1.62
% 1.21/1.62
% 1.21/1.62 Options Used:
% 1.21/1.62
% 1.21/1.62 useres = 1
% 1.21/1.62 useparamod = 1
% 1.21/1.62 useeqrefl = 1
% 1.21/1.62 useeqfact = 1
% 1.21/1.62 usefactor = 1
% 1.21/1.62 usesimpsplitting = 0
% 1.21/1.62 usesimpdemod = 5
% 1.21/1.62 usesimpres = 3
% 1.21/1.62
% 1.21/1.62 resimpinuse = 1000
% 1.21/1.62 resimpclauses = 20000
% 1.21/1.62 substype = eqrewr
% 1.21/1.62 backwardsubs = 1
% 1.21/1.62 selectoldest = 5
% 1.21/1.62
% 1.21/1.62 litorderings [0] = split
% 1.21/1.62 litorderings [1] = extend the termordering, first sorting on arguments
% 1.21/1.62
% 1.21/1.62 termordering = kbo
% 1.21/1.62
% 1.21/1.62 litapriori = 0
% 1.21/1.62 termapriori = 1
% 1.21/1.62 litaposteriori = 0
% 1.21/1.62 termaposteriori = 0
% 1.21/1.62 demodaposteriori = 0
% 1.21/1.62 ordereqreflfact = 0
% 1.21/1.62
% 1.21/1.62 litselect = negord
% 1.21/1.62
% 1.21/1.62 maxweight = 15
% 1.21/1.62 maxdepth = 30000
% 1.21/1.62 maxlength = 115
% 1.21/1.62 maxnrvars = 195
% 1.21/1.62 excuselevel = 1
% 1.21/1.62 increasemaxweight = 1
% 1.21/1.62
% 1.21/1.62 maxselected = 10000000
% 1.21/1.62 maxnrclauses = 10000000
% 1.21/1.62
% 1.21/1.62 showgenerated = 0
% 1.21/1.62 showkept = 0
% 1.21/1.62 showselected = 0
% 1.21/1.62 showdeleted = 0
% 1.21/1.62 showresimp = 1
% 1.21/1.62 showstatus = 2000
% 1.21/1.63
% 1.21/1.63 prologoutput = 1
% 1.21/1.63 nrgoals = 5000000
% 1.21/1.63 totalproof = 1
% 1.21/1.63
% 1.21/1.63 Symbols occurring in the translation:
% 1.21/1.63
% 1.21/1.63 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.21/1.63 . [1, 2] (w:1, o:161, a:1, s:1, b:0),
% 1.21/1.63 ! [4, 1] (w:0, o:90, a:1, s:1, b:0),
% 1.21/1.63 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.21/1.63 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.21/1.63 'class_Ring__and__Field_Oring' [40, 1] (w:1, o:95, a:1, s:1, b:0),
% 1.21/1.63 'c_HOL_Ouminus__class_Ouminus' [41, 1] (w:1, o:96, a:1, s:1, b:0),
% 1.21/1.63 'c_HOL_Otimes__class_Otimes' [43, 2] (w:1, o:186, a:1, s:1, b:0),
% 1.21/1.63 hAPP [45, 2] (w:1, o:187, a:1, s:1, b:0),
% 1.21/1.63 'class_OrderedGroup_Oab__group__add' [47, 1] (w:1, o:97, a:1, s:1, b:
% 1.21/1.63 0),
% 1.21/1.63 'c_HOL_Oplus__class_Oplus' [48, 1] (w:1, o:98, a:1, s:1, b:0),
% 1.21/1.63 'c_HOL_Ominus__class_Ominus' [49, 1] (w:1, o:99, a:1, s:1, b:0),
% 1.21/1.63 'c_OrderedGroup_Opordered__ab__group__add' [57, 7] (w:1, o:218, a:1
% 1.21/1.63 , s:1, b:0),
% 1.21/1.63 'class_OrderedGroup_Olordered__ab__group__add' [58, 1] (w:1, o:100
% 1.21/1.63 , a:1, s:1, b:0),
% 1.21/1.63 'c_lessequals' [59, 2] (w:1, o:188, a:1, s:1, b:0),
% 1.21/1.63 'c_HOL_Ozero__class_Ozero' [60, 1] (w:1, o:101, a:1, s:1, b:0),
% 1.21/1.63 hBOOL [61, 1] (w:1, o:102, a:1, s:1, b:0),
% 1.21/1.63 'class_OrderedGroup_Oab__semigroup__idem__mult' [62, 1] (w:1, o:103
% 1.21/1.63 , a:1, s:1, b:0),
% 1.21/1.63 'class_OrderedGroup_Opordered__ab__group__add' [65, 1] (w:1, o:105
% 1.21/1.63 , a:1, s:1, b:0),
% 1.21/1.63 'class_OrderedGroup_Oab__semigroup__mult' [66, 1] (w:1, o:106, a:1
% 1.21/1.63 , s:1, b:0),
% 1.21/1.63 'c_Fun_Ofcomp' [70, 5] (w:1, o:208, a:1, s:1, b:0),
% 1.21/1.63 'class_Ring__and__Field_Oordered__ring__strict' [71, 1] (w:1, o:109
% 1.21/1.63 , a:1, s:1, b:0),
% 1.21/1.63 'class_Ring__and__Field_Oordered__semiring__strict' [72, 1] (w:1, o:
% 1.21/1.63 110, a:1, s:1, b:0),
% 1.21/1.63 'c_HOL_Oord__class_Oless' [73, 2] (w:1, o:189, a:1, s:1, b:0),
% 1.21/1.63 'c_Ring__and__Field_Opordered__ring' [75, 8] (w:1, o:219, a:1, s:1
% 1.21/1.63 , b:0),
% 1.21/1.63 'class_OrderedGroup_Ocomm__monoid__add' [76, 1] (w:1, o:111, a:1, s:1
% 1.21/1.63 , b:0),
% 1.21/1.63 'c_Suc' [78, 0] (w:1, o:48, a:1, s:1, b:0),
% 1.21/1.63 'tc_nat' [80, 0] (w:1, o:52, a:1, s:1, b:0),
% 1.21/1.63 'c_SetInterval_Oord__class_OatLeastLessThan' [81, 3] (w:1, o:199, a:1
% 1.21/1.63 , s:1, b:0),
% 1.21/1.63 'c_Finite__Set_Osetsum' [82, 4] (w:1, o:205, a:1, s:1, b:0),
% 1.21/1.63 'class_Ring__and__Field_Oordered__semidom' [83, 1] (w:1, o:112, a:1
% 1.21/1.63 , s:1, b:0),
% 1.21/1.63 'class_Ring__and__Field_Omult__mono1' [84, 1] (w:1, o:113, a:1, s:1
% 1.21/1.63 , b:0),
% 1.21/1.63 'class_Ring__and__Field_Omult__mono' [85, 1] (w:1, o:114, a:1, s:1
% 1.21/1.63 , b:0),
% 1.21/1.63 'class_Ring__and__Field_Opordered__ring' [86, 1] (w:1, o:119, a:1, s:
% 1.21/1.63 1, b:0),
% 1.21/1.63 'class_RealVector_Oreal__normed__algebra' [87, 1] (w:1, o:120, a:1
% 1.21/1.63 , s:1, b:0),
% 1.21/1.63 'c_RealVector_Oadditive' [88, 3] (w:1, o:197, a:1, s:1, b:0),
% 1.21/1.63 'class_Orderings_Olinorder' [89, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.21/1.63 'c_Lattices_Oupper__semilattice__class_Osup' [90, 3] (w:1, o:200, a:1
% 1.21/1.63 , s:1, b:0),
% 1.21/1.63 'class_Ring__and__Field_Oidom' [91, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.21/1.63 'class_Int_Onumber__ring' [92, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.21/1.63 'class_Ring__and__Field_Oordered__field' [95, 1] (w:1, o:115, a:1, s:
% 1.21/1.63 1, b:0),
% 1.21/1.63 'class_Ring__and__Field_Odivision__by__zero' [96, 1] (w:1, o:127, a:1
% 1.21/1.63 , s:1, b:0),
% 1.21/1.63 'c_HOL_Oinverse__class_Odivide' [97, 3] (w:1, o:201, a:1, s:1, b:0),
% 1.21/1.63
% 1.21/1.63 'class_OrderedGroup_Osemigroup__mult' [99, 1] (w:1, o:128, a:1, s:1
% 1.21/1.63 , b:0),
% 1.21/1.63 'c_Ring__and__Field_Oring' [100, 6] (w:1, o:215, a:1, s:1, b:0),
% 1.21/1.63 'class_Ring__and__Field_Osemiring' [101, 1] (w:1, o:130, a:1, s:1, b:
% 1.21/1.63 0),
% 1.21/1.63 'class_Lattices_Oupper__semilattice' [102, 1] (w:1, o:131, a:1, s:1
% 1.21/1.63 , b:0),
% 1.21/1.63 'c_Ring__and__Field_Ofield' [106, 9] (w:1, o:220, a:1, s:1, b:0),
% 1.21/1.63 'c_SetInterval_Oord__class_OatMost' [108, 2] (w:1, o:191, a:1, s:1
% 1.21/1.63 , b:0),
% 1.21/1.63 'c_Finite__Set_Ofinite' [109, 2] (w:1, o:192, a:1, s:1, b:0),
% 1.21/1.63 'c_Fun_Ocomp' [113, 5] (w:1, o:209, a:1, s:1, b:0),
% 1.21/1.63 'class_Ring__and__Field_Ofield' [117, 1] (w:1, o:132, a:1, s:1, b:0)
% 1.21/1.63 ,
% 1.21/1.63 'class_RealVector_Oreal__normed__vector' [119, 1] (w:1, o:133, a:1
% 1.21/1.63 , s:1, b:0),
% 1.21/1.63 'c_RealVector_Obounded__bilinear' [121, 4] (w:1, o:206, a:1, s:1, b:0
% 11.51/11.87 ),
% 11.51/11.87 'c_Option_Ooption_ONone' [126, 1] (w:1, o:134, a:1, s:1, b:0),
% 11.51/11.87 'c_Option_Ooption_Ooption__case' [127, 5] (w:1, o:210, a:1, s:1, b:0)
% 11.51/11.87 ,
% 11.51/11.87 'c_SetInterval_Oord__class_OlessThan' [128, 2] (w:1, o:193, a:1, s:1
% 11.51/11.87 , b:0),
% 11.51/11.87 'class_RealVector_Oreal__vector' [129, 1] (w:1, o:135, a:1, s:1, b:0)
% 11.51/11.87 ,
% 11.51/11.87 'c_RealVector_OscaleR__class_OscaleR' [130, 2] (w:1, o:190, a:1, s:1
% 11.51/11.87 , b:0),
% 11.51/11.87 'class_Ring__and__Field_Oordered__idom' [132, 1] (w:1, o:116, a:1, s:
% 11.51/11.87 1, b:0),
% 11.51/11.87 'class_Orderings_Oorder' [133, 1] (w:1, o:136, a:1, s:1, b:0),
% 11.51/11.87 'v_n' [135, 0] (w:1, o:68, a:1, s:1, b:0),
% 11.51/11.87 'class_Lattices_Oboolean__algebra' [136, 1] (w:1, o:137, a:1, s:1, b:
% 11.51/11.87 0),
% 11.51/11.87 'class_OrderedGroup_Ogroup__add' [137, 1] (w:1, o:138, a:1, s:1, b:0)
% 11.51/11.87 ,
% 11.51/11.87 'class_Ring__and__Field_Ocomm__semiring__1' [138, 1] (w:1, o:125, a:1
% 11.51/11.87 , s:1, b:0),
% 11.51/11.87 'class_OrderedGroup_Opordered__comm__monoid__add' [144, 1] (w:1, o:
% 11.51/11.87 139, a:1, s:1, b:0),
% 11.51/11.87 'class_Ring__and__Field_Opordered__cancel__semiring' [146, 1] (w:1
% 11.51/11.87 , o:140, a:1, s:1, b:0),
% 11.51/11.87 'class_OrderedGroup_Oordered__ab__group__add' [147, 1] (w:1, o:104
% 11.51/11.87 , a:1, s:1, b:0),
% 11.51/11.87 'v_k' [148, 0] (w:1, o:72, a:1, s:1, b:0),
% 11.51/11.87 't_a' [149, 0] (w:1, o:73, a:1, s:1, b:0),
% 11.51/11.87 'c_Map_Omap__comp' [150, 6] (w:1, o:217, a:1, s:1, b:0),
% 11.51/11.87 'tc_Option_Ooption' [151, 1] (w:1, o:141, a:1, s:1, b:0),
% 11.51/11.87 'class_Ring__and__Field_Opordered__semiring' [155, 1] (w:1, o:142, a:
% 11.51/11.87 1, s:1, b:0),
% 11.51/11.87 'c_SetInterval_Oord__class_OgreaterThanLessThan' [158, 3] (w:1, o:202
% 11.51/11.87 , a:1, s:1, b:0),
% 11.51/11.87 'class_Divides_Oring__div' [159, 1] (w:1, o:143, a:1, s:1, b:0),
% 11.51/11.87 'c_Divides_Odiv__class_Omod' [160, 3] (w:1, o:203, a:1, s:1, b:0),
% 11.51/11.87 'c_RealVector_Ovector__space' [162, 3] (w:1, o:198, a:1, s:1, b:0),
% 11.51/11.87 'class_Ring__and__Field_Oring__no__zero__divisors' [163, 1] (w:1, o:
% 11.51/11.87 129, a:1, s:1, b:0),
% 11.51/11.87 'class_Ring__and__Field_Ono__zero__divisors' [164, 1] (w:1, o:108, a:
% 11.51/11.87 1, s:1, b:0),
% 11.51/11.87 'class_RealVector_Oreal__normed__field' [166, 1] (w:1, o:144, a:1, s:
% 11.51/11.87 1, b:0),
% 11.51/11.87 'class_Ring__and__Field_Oordered__semiring' [168, 1] (w:1, o:117, a:1
% 11.51/11.87 , s:1, b:0),
% 11.51/11.87 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [169, 1]
% 11.51/11.87 (w:1, o:145, a:1, s:1, b:0),
% 11.51/11.87 'class_Divides_Osemiring__div' [170, 1] (w:1, o:146, a:1, s:1, b:0),
% 11.51/11.87
% 11.51/11.87 'class_Lattices_Olattice' [171, 1] (w:1, o:147, a:1, s:1, b:0),
% 11.51/11.87 'c_COMBB' [172, 5] (w:1, o:211, a:1, s:1, b:0),
% 11.51/11.87 'class_Ring__and__Field_Osemiring__0' [173, 1] (w:1, o:148, a:1, s:1
% 11.51/11.87 , b:0),
% 11.51/11.87 'class_RealVector_Oreal__algebra' [174, 1] (w:1, o:149, a:1, s:1, b:0
% 11.51/11.87 ),
% 11.51/11.87 'class_RealVector_Oreal__field' [175, 1] (w:1, o:150, a:1, s:1, b:0)
% 11.51/11.87 ,
% 11.51/11.87 'tc_fun' [177, 2] (w:1, o:194, a:1, s:1, b:0),
% 11.51/11.87 'c_COMBS' [178, 5] (w:1, o:212, a:1, s:1, b:0),
% 11.51/11.87 'class_Orderings_Opreorder' [181, 1] (w:1, o:151, a:1, s:1, b:0),
% 11.51/11.87 't_b' [184, 0] (w:1, o:76, a:1, s:1, b:0),
% 11.51/11.87 'class_Ring__and__Field_Omult__zero' [187, 1] (w:1, o:107, a:1, s:1
% 11.51/11.87 , b:0),
% 11.51/11.87 'c_OrderedGroup_Osemigroup__add' [188, 2] (w:1, o:195, a:1, s:1, b:0)
% 11.51/11.87 ,
% 11.51/11.87 'v_x' [189, 0] (w:1, o:77, a:1, s:1, b:0),
% 11.51/11.87 'class_Finite__Set_Ofinite_Ofinite' [190, 1] (w:1, o:152, a:1, s:1
% 11.51/11.87 , b:0),
% 11.51/11.87 'class_Ring__and__Field_Oordered__comm__semiring__strict' [191, 1]
% 11.51/11.87 (w:1, o:118, a:1, s:1, b:0),
% 11.51/11.87 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [192, 1]
% 11.51/11.87 (w:1, o:153, a:1, s:1, b:0),
% 11.51/11.87 'class_OrderedGroup_Oab__semigroup__add' [193, 1] (w:1, o:154, a:1
% 11.51/11.87 , s:1, b:0),
% 11.51/11.87 'class_OrderedGroup_Osemigroup__add' [194, 1] (w:1, o:155, a:1, s:1
% 11.51/11.87 , b:0),
% 11.51/11.87 'class_OrderedGroup_Opordered__ab__semigroup__add' [195, 1] (w:1, o:
% 11.51/11.87 156, a:1, s:1, b:0),
% 11.51/11.87 'class_Ring__and__Field_Ocomm__semiring' [196, 1] (w:1, o:126, a:1
% 11.51/11.87 , s:1, b:0),
% 11.51/11.87 'class_OrderedGroup_Olordered__ab__group__add__join' [197, 1] (w:1
% 11.51/11.87 , o:157, a:1, s:1, b:0),
% 11.51/11.87 'class_OrderedGroup_Ocancel__ab__semigroup__add' [198, 1] (w:1, o:158
% 11.51/11.87 , a:1, s:1, b:0),
% 45.62/45.96 'c_OrderedGroup_Ocancel__ab__semigroup__add__axioms' [199, 2] (w:1
% 45.62/45.96 , o:196, a:1, s:1, b:0),
% 45.62/45.96 'class_OrderedGroup_Omonoid__add' [200, 1] (w:1, o:159, a:1, s:1, b:0
% 45.62/45.96 ),
% 45.62/45.96 'c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1' [201, 5] (w:1
% 45.62/45.96 , o:213, a:1, s:1, b:0),
% 45.62/45.96 'c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1' [202, 5] (w:1
% 45.62/45.96 , o:214, a:1, s:1, b:0),
% 45.62/45.96 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__singleton__1' [203
% 45.62/45.96 , 4] (w:1, o:207, a:1, s:1, b:0),
% 45.62/45.96 'class_HOL_Oord' [204, 1] (w:1, o:123, a:1, s:1, b:0),
% 45.62/45.96 'c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1' [205, 6] (w:1
% 45.62/45.96 , o:216, a:1, s:1, b:0),
% 45.62/45.96 'v_f' [207, 0] (w:1, o:79, a:1, s:1, b:0),
% 45.62/45.96 'v_g' [208, 0] (w:1, o:80, a:1, s:1, b:0),
% 45.62/45.96 't_c' [209, 0] (w:1, o:81, a:1, s:1, b:0),
% 45.62/45.96 'v_m' [210, 0] (w:1, o:67, a:1, s:1, b:0),
% 45.62/45.96 'v_h' [211, 0] (w:1, o:82, a:1, s:1, b:0),
% 45.62/45.96 'class_OrderedGroup_Ocancel__semigroup__add' [212, 1] (w:1, o:160, a:
% 45.62/45.96 1, s:1, b:0),
% 45.62/45.96 'tc_bool' [216, 0] (w:1, o:86, a:1, s:1, b:0),
% 45.62/45.96 'tc_RealDef_Oreal' [217, 0] (w:1, o:87, a:1, s:1, b:0),
% 45.62/45.96 'c_fequal' [218, 3] (w:1, o:204, a:1, s:1, b:0).
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Starting Search:
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 6494
% 45.62/45.96 Kept: 2495
% 45.62/45.96 Inuse: 155
% 45.62/45.96 Deleted: 1
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 12104
% 45.62/45.96 Kept: 5102
% 45.62/45.96 Inuse: 218
% 45.62/45.96 Deleted: 4
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 17635
% 45.62/45.96 Kept: 7124
% 45.62/45.96 Inuse: 330
% 45.62/45.96 Deleted: 6
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 30273
% 45.62/45.96 Kept: 9757
% 45.62/45.96 Inuse: 389
% 45.62/45.96 Deleted: 7
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 41146
% 45.62/45.96 Kept: 11958
% 45.62/45.96 Inuse: 409
% 45.62/45.96 Deleted: 7
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 66038
% 45.62/45.96 Kept: 16286
% 45.62/45.96 Inuse: 424
% 45.62/45.96 Deleted: 7
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 88984
% 45.62/45.96 Kept: 19185
% 45.62/45.96 Inuse: 429
% 45.62/45.96 Deleted: 7
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 115034
% 45.62/45.96 Kept: 22142
% 45.62/45.96 Inuse: 434
% 45.62/45.96 Deleted: 7
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96 Resimplifying clauses:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 142372
% 45.62/45.96 Kept: 25114
% 45.62/45.96 Inuse: 439
% 45.62/45.96 Deleted: 77
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 187754
% 45.62/45.96 Kept: 28281
% 45.62/45.96 Inuse: 444
% 45.62/45.96 Deleted: 77
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 237547
% 45.62/45.96 Kept: 31507
% 45.62/45.96 Inuse: 449
% 45.62/45.96 Deleted: 77
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 255553
% 45.62/45.96 Kept: 33522
% 45.62/45.96 Inuse: 471
% 45.62/45.96 Deleted: 77
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 270946
% 45.62/45.96 Kept: 35576
% 45.62/45.96 Inuse: 489
% 45.62/45.96 Deleted: 77
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 357887
% 45.62/45.96 Kept: 39903
% 45.62/45.96 Inuse: 494
% 45.62/45.96 Deleted: 77
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 413787
% 45.62/45.96 Kept: 43598
% 45.62/45.96 Inuse: 499
% 45.62/45.96 Deleted: 77
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96 Resimplifying clauses:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 520922
% 45.62/45.96 Kept: 48234
% 45.62/45.96 Inuse: 504
% 45.62/45.96 Deleted: 97
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 542831
% 45.62/45.96 Kept: 50314
% 45.62/45.96 Inuse: 529
% 45.62/45.96 Deleted: 97
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 567604
% 45.62/45.96 Kept: 52704
% 45.62/45.96 Inuse: 549
% 45.62/45.96 Deleted: 97
% 45.62/45.96 Deletedinuse: 0
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96 Resimplifying inuse:
% 45.62/45.96 Done
% 45.62/45.96
% 45.62/45.96
% 45.62/45.96 Intermediate Status:
% 45.62/45.96 Generated: 588468
% 104.78/105.18 Kept: 54966
% 104.78/105.18 Inuse: 564
% 104.78/105.18 Deleted: 97
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 614473
% 104.78/105.18 Kept: 57833
% 104.78/105.18 Inuse: 579
% 104.78/105.18 Deleted: 97
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 634315
% 104.78/105.18 Kept: 60164
% 104.78/105.18 Inuse: 594
% 104.78/105.18 Deleted: 97
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 646560
% 104.78/105.18 Kept: 62578
% 104.78/105.18 Inuse: 609
% 104.78/105.18 Deleted: 97
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying clauses:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 658482
% 104.78/105.18 Kept: 65281
% 104.78/105.18 Inuse: 624
% 104.78/105.18 Deleted: 182
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 669328
% 104.78/105.18 Kept: 67542
% 104.78/105.18 Inuse: 639
% 104.78/105.18 Deleted: 182
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 681602
% 104.78/105.18 Kept: 70157
% 104.78/105.18 Inuse: 659
% 104.78/105.18 Deleted: 182
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 692462
% 104.78/105.18 Kept: 72532
% 104.78/105.18 Inuse: 674
% 104.78/105.18 Deleted: 182
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 700925
% 104.78/105.18 Kept: 74589
% 104.78/105.18 Inuse: 689
% 104.78/105.18 Deleted: 182
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 710195
% 104.78/105.18 Kept: 77158
% 104.78/105.18 Inuse: 704
% 104.78/105.18 Deleted: 182
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 717273
% 104.78/105.18 Kept: 79276
% 104.78/105.18 Inuse: 715
% 104.78/105.18 Deleted: 182
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 724282
% 104.78/105.18 Kept: 81369
% 104.78/105.18 Inuse: 726
% 104.78/105.18 Deleted: 182
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 732252
% 104.78/105.18 Kept: 83677
% 104.78/105.18 Inuse: 739
% 104.78/105.18 Deleted: 182
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying clauses:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 753744
% 104.78/105.18 Kept: 88029
% 104.78/105.18 Inuse: 759
% 104.78/105.18 Deleted: 210
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 766843
% 104.78/105.18 Kept: 90553
% 104.78/105.18 Inuse: 764
% 104.78/105.18 Deleted: 210
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 779649
% 104.78/105.18 Kept: 93030
% 104.78/105.18 Inuse: 769
% 104.78/105.18 Deleted: 210
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 790905
% 104.78/105.18 Kept: 95196
% 104.78/105.18 Inuse: 784
% 104.78/105.18 Deleted: 210
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 803134
% 104.78/105.18 Kept: 97198
% 104.78/105.18 Inuse: 802
% 104.78/105.18 Deleted: 210
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 810510
% 104.78/105.18 Kept: 99217
% 104.78/105.18 Inuse: 812
% 104.78/105.18 Deleted: 210
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 820755
% 104.78/105.18 Kept: 101255
% 104.78/105.18 Inuse: 824
% 104.78/105.18 Deleted: 210
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 837110
% 104.78/105.18 Kept: 103629
% 104.78/105.18 Inuse: 844
% 104.78/105.18 Deleted: 210
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying clauses:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 851921
% 104.78/105.18 Kept: 105782
% 104.78/105.18 Inuse: 869
% 104.78/105.18 Deleted: 258
% 104.78/105.18 Deletedinuse: 0
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 866970
% 104.78/105.18 Kept: 108876
% 104.78/105.18 Inuse: 888
% 104.78/105.18 Deleted: 262
% 104.78/105.18 Deletedinuse: 3
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 879663
% 104.78/105.18 Kept: 110937
% 104.78/105.18 Inuse: 908
% 104.78/105.18 Deleted: 262
% 104.78/105.18 Deletedinuse: 3
% 104.78/105.18
% 104.78/105.18
% 104.78/105.18 Intermediate Status:
% 104.78/105.18 Generated: 916854
% 104.78/105.18 Kept: 114391
% 104.78/105.18 Inuse: 913
% 104.78/105.18 Deleted: 262
% 104.78/105.18 Deletedinuse: 3
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 104.78/105.18 Done
% 104.78/105.18
% 104.78/105.18 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 935683
% 223.99/224.37 Kept: 116994
% 223.99/224.37 Inuse: 933
% 223.99/224.37 Deleted: 262
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 950383
% 223.99/224.37 Kept: 119103
% 223.99/224.37 Inuse: 943
% 223.99/224.37 Deleted: 262
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 959945
% 223.99/224.37 Kept: 121208
% 223.99/224.37 Inuse: 953
% 223.99/224.37 Deleted: 262
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 970072
% 223.99/224.37 Kept: 123324
% 223.99/224.37 Inuse: 963
% 223.99/224.37 Deleted: 262
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying clauses:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 979417
% 223.99/224.37 Kept: 125544
% 223.99/224.37 Inuse: 973
% 223.99/224.37 Deleted: 788
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 994868
% 223.99/224.37 Kept: 128050
% 223.99/224.37 Inuse: 983
% 223.99/224.37 Deleted: 788
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1007392
% 223.99/224.37 Kept: 130113
% 223.99/224.37 Inuse: 997
% 223.99/224.37 Deleted: 788
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1013495
% 223.99/224.37 Kept: 132160
% 223.99/224.37 Inuse: 1004
% 223.99/224.37 Deleted: 788
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1025537
% 223.99/224.37 Kept: 134553
% 223.99/224.37 Inuse: 1008
% 223.99/224.37 Deleted: 788
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1032243
% 223.99/224.37 Kept: 136696
% 223.99/224.37 Inuse: 1016
% 223.99/224.37 Deleted: 788
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1040335
% 223.99/224.37 Kept: 139242
% 223.99/224.37 Inuse: 1023
% 223.99/224.37 Deleted: 788
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1054940
% 223.99/224.37 Kept: 141448
% 223.99/224.37 Inuse: 1043
% 223.99/224.37 Deleted: 788
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1073066
% 223.99/224.37 Kept: 143789
% 223.99/224.37 Inuse: 1053
% 223.99/224.37 Deleted: 788
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1087698
% 223.99/224.37 Kept: 146063
% 223.99/224.37 Inuse: 1058
% 223.99/224.37 Deleted: 788
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying clauses:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1107836
% 223.99/224.37 Kept: 148139
% 223.99/224.37 Inuse: 1073
% 223.99/224.37 Deleted: 793
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1120039
% 223.99/224.37 Kept: 150226
% 223.99/224.37 Inuse: 1082
% 223.99/224.37 Deleted: 793
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1132129
% 223.99/224.37 Kept: 152271
% 223.99/224.37 Inuse: 1089
% 223.99/224.37 Deleted: 793
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1142242
% 223.99/224.37 Kept: 154682
% 223.99/224.37 Inuse: 1098
% 223.99/224.37 Deleted: 793
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1151751
% 223.99/224.37 Kept: 157111
% 223.99/224.37 Inuse: 1108
% 223.99/224.37 Deleted: 793
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1158463
% 223.99/224.37 Kept: 159113
% 223.99/224.37 Inuse: 1115
% 223.99/224.37 Deleted: 793
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1167805
% 223.99/224.37 Kept: 162009
% 223.99/224.37 Inuse: 1123
% 223.99/224.37 Deleted: 793
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1175885
% 223.99/224.37 Kept: 164145
% 223.99/224.37 Inuse: 1132
% 223.99/224.37 Deleted: 793
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1182296
% 223.99/224.37 Kept: 166286
% 223.99/224.37 Inuse: 1137
% 223.99/224.37 Deleted: 793
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying clauses:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1188022
% 223.99/224.37 Kept: 168337
% 223.99/224.37 Inuse: 1141
% 223.99/224.37 Deleted: 1107
% 223.99/224.37 Deletedinuse: 3
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37 Resimplifying inuse:
% 223.99/224.37 Done
% 223.99/224.37
% 223.99/224.37
% 223.99/224.37 Intermediate Status:
% 223.99/224.37 Generated: 1194500
% 223.99/224.37 Kept: 170458
% 223.99/224.37 Inuse: 1147
% 223.99/224.37 Deleted: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------