TSTP Solution File: SWV875-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV875-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 16:28:58 EDT 2022
% Result : Unsatisfiable 1.18s 1.62s
% Output : Refutation 1.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SWV875-1 : TPTP v8.1.0. Released v4.1.0.
% 0.13/0.14 % Command : bliksem %s
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % DateTime : Thu Jun 16 03:30:10 EDT 2022
% 0.15/0.36 % CPUTime :
% 1.18/1.58 *** allocated 10000 integers for termspace/termends
% 1.18/1.58 *** allocated 10000 integers for clauses
% 1.18/1.58 *** allocated 10000 integers for justifications
% 1.18/1.58 *** allocated 15000 integers for termspace/termends
% 1.18/1.58 *** allocated 22500 integers for termspace/termends
% 1.18/1.58 *** allocated 33750 integers for termspace/termends
% 1.18/1.58 Bliksem 1.12
% 1.18/1.58
% 1.18/1.58
% 1.18/1.58 Automatic Strategy Selection
% 1.18/1.58
% 1.18/1.58 Clauses:
% 1.18/1.58 [
% 1.18/1.58 [ ~( =( hAPP( hAPP( X, Y ), Z ), Y ) ), ~(
% 1.18/1.58 'c_Lattices_Olower__semilattice'( T, U, X, W ) ), hBOOL( hAPP( hAPP( T, Y
% 1.18/1.58 ), Z ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( hBOOL( hAPP( hAPP( T, Z ), Y ) ) )
% 1.18/1.58 , ~( 'c_Lattices_Olower__semilattice'( T, U, X, W ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.58 ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.58 ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), T ), Z ) ) ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y )
% 1.18/1.58 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y )
% 1.18/1.58 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y )
% 1.18/1.58 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y )
% 1.18/1.58 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.58 ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.58 ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), T ), Z ) ) ) )
% 1.18/1.58 ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.58 X, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.58 X, 'tc_bool' ) ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 'tc_fun'( X, 'tc_bool' ) ), T ), Y ) ) ) ],
% 1.18/1.58 [ ~( =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.58 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.58 X, 'tc_bool' ) ), Z ), T ) ) ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 'tc_fun'( X, 'tc_bool' ) ), T ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.18/1.58 'c_OrderedGroup_Oab__semigroup__idem__mult'(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), X ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) )
% 1.18/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.58 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, X ) ),
% 1.18/1.58 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, U, X ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Y ) ) )
% 1.18/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.58 'c_SetInterval_Oord__class_OatLeastAtMost'( T, Y, X ) ),
% 1.18/1.58 'c_SetInterval_Oord__class_OatLeastAtMost'( U, Z, X ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Y
% 1.18/1.58 , Z, X ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( T, U, X ) ) ),
% 1.18/1.58 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_lessequals'( X ), T ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Ofold__image'(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.18/1.58 , T ) ), 'c_Finite__Set_Ofold__image'( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ), U, X, T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Ofold__image'(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( T,
% 1.18/1.58 'tc_bool' ) ), Z ), U ), X, T ) ), 'c_Finite__Set_Ofold__image'(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( T,
% 1.18/1.58 'tc_bool' ) ), Z ), U ), X, T ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) )
% 1.18/1.58 , ~( 'c_Finite__Set_Ofinite'( Z, T ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.58 Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omax'( X ), T ), Z ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.58 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.58 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.58 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.58 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.58 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ),
% 1.18/1.58 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ),
% 1.18/1.58 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.58 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.18/1.58 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ =( 'c_The'( hAPP( 'c_COMBC'( 'c_fequal'( X ), X, X, 'tc_bool' ), Y ),
% 1.18/1.58 X ), Y ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.18/1.58 [ =( 'c_Finite__Set_Ofold'( X, Y, Z, T, U ), 'c_The'(
% 1.18/1.58 'c_Finite__Set_Ofold__graph'( X, Y, Z, T, U ), U ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.18/1.58 ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.18/1.58 , Z, X ) ), T ) ), U ) ), W ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.58 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Z ), T ) ), W ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X
% 1.18/1.58 ) ), Z ) ), T ) ), W ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ) ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T )
% 1.18/1.58 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X
% 1.18/1.58 ) ), Z ) ), W ) ) ) ) ],
% 1.18/1.58 [ ~( =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ), T ) ) ), =( Y
% 1.18/1.58 , U ), =( hAPP( 'c_Fun_Ofun__upd'( X, U, hAPP( 'c_Option_Ooption_OSome'(
% 1.18/1.58 Z ), W ), V0, 'tc_Option_Ooption'( Z ) ), Y ), hAPP(
% 1.18/1.58 'c_Option_Ooption_OSome'( Z ), T ) ) ],
% 1.18/1.58 [ ~( =( hAPP( 'c_Fun_Ofun__upd'( X, Y, hAPP( 'c_Option_Ooption_OSome'( Z
% 1.18/1.58 ), T ), U, 'tc_Option_Ooption'( Z ) ), W ), hAPP(
% 1.18/1.58 'c_Option_Ooption_OSome'( Z ), V0 ) ) ), =( hAPP( X, W ), hAPP(
% 1.18/1.58 'c_Option_Ooption_OSome'( Z ), V0 ) ), =( T, V0 ) ],
% 1.18/1.58 [ ~( =( hAPP( 'c_Fun_Ofun__upd'( X, Y, hAPP( 'c_Option_Ooption_OSome'( Z
% 1.18/1.58 ), T ), U, 'tc_Option_Ooption'( Z ) ), W ), hAPP(
% 1.18/1.58 'c_Option_Ooption_OSome'( Z ), V0 ) ) ), =( hAPP( X, W ), hAPP(
% 1.18/1.58 'c_Option_Ooption_OSome'( Z ), V0 ) ), =( W, Y ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( =( 'c_Fun_Ofun__upd'( X, Y, hAPP( 'c_Option_Ooption_OSome'( Z ), T
% 1.18/1.58 ), U, 'tc_Option_Ooption'( Z ) ), 'c_COMBK'( 'c_Option_Ooption_ONone'( Z
% 1.18/1.58 ), 'tc_Option_Ooption'( Z ), U ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.58 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z
% 1.18/1.58 ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ), ~(
% 1.18/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.58 , T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.58 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z
% 1.18/1.58 ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ), ~(
% 1.18/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.58 , Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omax'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omax'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_HOL_Oord'( X ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.18/1.58 'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_HOL_Oord'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.18/1.58 X ), Y ), 'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( hBOOL( hAPP( hAPP( T, Y ), Z ) ) )
% 1.18/1.58 , ~( 'c_Lattices_Olower__semilattice'( T, U, X, W ) ) ],
% 1.18/1.58 [ 'c_Map_Omap__le'( 'c_Fun_Ofun__upd'( X, Y, Z, T, 'tc_Option_Ooption'(
% 1.18/1.58 U ) ), 'c_Fun_Ofun__upd'( W, Y, Z, T, 'tc_Option_Ooption'( U ) ), T, U )
% 1.18/1.58 , ~( 'c_Map_Omap__le'( X, W, T, U ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), =( Z,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), =( Y,
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.18/1.58 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.58 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ) ) ), ~( hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), T ), U ) ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.58 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ), W ) ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.58 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), T ) ), U ) ), W ) ), ~( hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), T ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.58 , Z ), T ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) )
% 1.18/1.58 ), ~( 'c_Finite__Set_Ofinite'( T, Y ) ), ~( 'c_Finite__Set_Ofinite'( Z,
% 1.18/1.58 Y ) ), =( 'c_Finite__Set_Osetsum'( U, hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.58 , Z ), T ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.58 'c_Finite__Set_Osetsum'( U, Z, Y, X ) ), 'c_Finite__Set_Osetsum'( U, T, Y
% 1.18/1.58 , X ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Y
% 1.18/1.58 , Z, X ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( T, U, X ) ) ),
% 1.18/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.58 T ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), T ), Y ) ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.18/1.58 'c_OrderedGroup_Oab__semigroup__idem__mult'(
% 1.18/1.58 'c_Orderings_Oord__class_Omax'( X ), X ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ =( 'c_Fun_Ofun__upd'( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), W, V0, T, U
% 1.18/1.58 ), 'c_Fun_Ofun__upd'( 'c_Fun_Ofun__upd'( X, W, V0, T, U ), Y, Z, T, U )
% 1.18/1.58 ), =( Y, W ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.58 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.58 ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~(
% 1.18/1.58 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.58 ) ],
% 1.18/1.58 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.58 ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.18/1.58 ), 'c_Finite__Set_Ocard'( Y, X ) ), 'c_Finite__Set_Ocard'( Z, X ) ) ) )
% 1.18/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.58 Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.58 ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), T ), Y ) ), Z ) ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.58 ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ), Z ) ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.18/1.58 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.18/1.58 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.18/1.58 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.18/1.58 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.58 ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), T ), Y ) ), Z ) ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.58 ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ), Z ) ) )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omax'( X ), T ), Z ) ) ) ) ],
% 1.18/1.58 [ ~( hBOOL( hAPP( X, 'c_Option_Ooption_Ooption__case'( Y, Z, hAPP(
% 1.18/1.58 'c_Option_Ooption_OSome'( 't_b' ), T ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP(
% 1.18/1.58 X, hAPP( Z, T ) ) ) ],
% 1.18/1.58 [ ~( hBOOL( hAPP( X, 'c_Option_Ooption_Ooption__case'( Y, Z, hAPP(
% 1.18/1.58 'c_Option_Ooption_OSome'( 't_b' ), T ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP(
% 1.18/1.58 X, hAPP( Z, T ) ) ) ],
% 1.18/1.58 [ =( 'c_Map_Orestrict__map'( 'c_Fun_Ofun__upd'( X, Y, Z, T,
% 1.18/1.58 'tc_Option_Ooption'( U ) ), W, T, U ), 'c_Map_Orestrict__map'( X, W, T, U
% 1.18/1.58 ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), W ) ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.58 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.58 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.58 X, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.58 X, 'tc_bool' ) ), Z ), T ) ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.58 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Z ), T ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.58 'tc_fun'( X, 'tc_bool' ) ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.18/1.58 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.18/1.58 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.18/1.58 'c_Orderings_Oord__class_Omax'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), T ), Y ) ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.58 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.18/1.58 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.58 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.18/1.58 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.18/1.58 [ =( 'c_Map_Orestrict__map'( 'c_Map_Orestrict__map'( X, Y, Z, T ), U, Z
% 1.18/1.58 , T ), 'c_Map_Orestrict__map'( X, hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.18/1.58 , Y ), U ), Z, T ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.58 'c_Finite__Set_Osetsum'( Y, Z, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.58 , 'c_Finite__Set_Ofinite'( Z, T ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.58 'c_Finite__Set_Osetsum'( Y, Z, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.58 , 'c_Finite__Set_Ofinite'( Z, T ) ],
% 1.18/1.58 [ =( X, Y ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X
% 1.18/1.58 ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X
% 1.18/1.58 ), 'c_Suc'( Y ) ) ) ) ],
% 1.18/1.58 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.58 , Y ), 'c_Suc'( X ) ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'tc_nat' ), Y ), X ) ) ],
% 1.18/1.58 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.58 , X ), 'c_Suc'( Y ) ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.58 'tc_nat' ), X ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.18/1.58 [ =( hAPP( 'c_Map_Orestrict__map'( 'c_COMBK'( 'c_Option_Ooption_ONone'(
% 1.18/1.58 X ), 'tc_Option_Ooption'( X ), 't_a' ), Y, 't_a', X ), 'v_x' ),
% 1.18/1.58 'c_Option_Ooption_ONone'( X ) ) ],
% 1.18/1.58 [ =( 'c_Map_Orestrict__map'( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), T
% 1.18/1.58 ), Y, U ), 'c_Fun_Ofun__upd'( 'c_Map_Orestrict__map'( X, T, Y, U ), Z,
% 1.18/1.58 hAPP( X, Z ), Y, 'tc_Option_Ooption'( U ) ) ) ],
% 1.18/1.58 [ 'c_Orderings_Olinorder'( 'c_COMBC'( X, Y, Y, 'tc_bool' ), 'c_COMBC'( Z
% 1.18/1.58 , Y, Y, 'tc_bool' ), Y ), ~( 'c_Orderings_Olinorder'( X, Z, Y ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.58 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.58 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.58 X, 'tc_bool' ) ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X,
% 1.18/1.58 'tc_bool' ) ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.58 'tc_fun'( X, 'tc_bool' ) ), Y ), T ), 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.58 X, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X,
% 1.18/1.58 'tc_bool' ) ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Y ), T ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.58 'tc_fun'( X, 'tc_bool' ) ), Z ), T ), 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.18/1.58 'c_Finite__Set_Ofold'( 'c_Lattices_Olower__semilattice__class_Oinf'( X )
% 1.18/1.58 , Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ), X, X ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ),
% 1.18/1.58 'c_Finite__Set_Ofold'( 'c_Lattices_Olower__semilattice__class_Oinf'( X )
% 1.18/1.58 , Y, T, X, X ) ) ), ~( 'c_Finite__Set_Ofinite'( T, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.58 'c_Finite__Set_Osetsum'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.18/1.58 'tc_bool' ) ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ =( 'c_Fun_Ofun__upd'( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), Y, W, T, U )
% 1.18/1.58 , 'c_Fun_Ofun__upd'( X, Y, W, T, U ) ) ],
% 1.18/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.58 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.58 'c_HOL_Ominus__class_Ominus'( T, U, 'tc_fun'( X, 'tc_bool' ) ) ) ), ~(
% 1.18/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), U ), Z ) )
% 1.18/1.58 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y )
% 1.18/1.58 , T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 X ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ),
% 1.18/1.58 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) )
% 1.18/1.58 ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP(
% 1.18/1.58 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.58 'tc_fun'( X, 'tc_bool' ) ), T ), Z ), 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.58 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.58 ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X,
% 1.18/1.58 'tc_bool' ) ), Y ), Y ) ) ) ],
% 1.18/1.58 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), X )
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), X )
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_HOL_Oord'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'tc_fun'( Y, X ) ), Z ), T ) ), hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_lessequals'( 'tc_fun'( Y, X ) ), T ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_lessequals'( 'tc_fun'( Y, X ) ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), Y ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), Y ), Y ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.58 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ),
% 1.18/1.58 'c_SetInterval_Oord__class_OatLeastAtMost'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_lessequals'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 X ), T ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.58 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ),
% 1.18/1.58 'c_SetInterval_Oord__class_OatLeastAtMost'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_lessequals'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 X ), T ), Y ) ) ) ],
% 1.18/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z
% 1.18/1.58 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.58 hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool' ), 'tc_bool' ), Y
% 1.18/1.58 ) ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool' ),
% 1.18/1.58 'tc_bool' ), Z ) ) ) ) ],
% 1.18/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.18/1.58 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool' ), 'tc_bool' ), Y ) ),
% 1.18/1.58 hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool' ), 'tc_bool' ), Z
% 1.18/1.58 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Y ), Z ) ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ),
% 1.18/1.58 Z ) ), ~( 'c_OrderedGroup_Oab__semigroup__idem__mult'( X, T ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Y ), Y ), ~(
% 1.18/1.58 'c_OrderedGroup_Oab__semigroup__idem__mult'( X, Z ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), =( Z, Y ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.58 'c_Finite__Set_Osetsum'( 'c_COMBK'( 'c_HOL_Ozero__class_Ozero'( X ), X, Y
% 1.18/1.58 ), Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.58 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.18/1.58 'c_Finite__Set_Ocard'( X, Y ) ), 'c_Finite__Set_Ocard'( Z, Y ) ) ), ~(
% 1.18/1.58 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.58 , X ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ],
% 1.18/1.58 [ =( 'c_Map_Odom'( 'c_Map_Orestrict__map'( X, Y, Z, T ), Z, T ), hAPP(
% 1.18/1.58 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z,
% 1.18/1.58 'tc_bool' ) ), 'c_Map_Odom'( X, Z, T ) ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.18/1.58 , Z ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.18/1.58 , Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y )
% 1.18/1.58 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ),
% 1.18/1.58 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y )
% 1.18/1.58 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ),
% 1.18/1.58 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y )
% 1.18/1.58 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ),
% 1.18/1.58 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X
% 1.18/1.58 ) ), Z ) ), T ), W ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X
% 1.18/1.58 ) ), Z ) ), W ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( T, Y, X
% 1.18/1.58 ) ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Y ), Y ), ~( 'c_Lattices_Olower__semilattice'(
% 1.18/1.58 Z, T, X, U ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.18/1.58 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Lattices_Olower__semilattice'( U, W, X
% 1.18/1.58 , V0 ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.18/1.58 'c_Lattices_Olower__semilattice'( T, U, X, W ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ),
% 1.18/1.58 Z ) ), ~( 'c_Lattices_Olower__semilattice'( T, U, X, W ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.18/1.58 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Lattices_Olower__semilattice'( U, W, X
% 1.18/1.58 , V0 ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y, hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.18/1.58 , T ), U ), Z, X ) ), 'c_Finite__Set_Osetsum'( Y, hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.18/1.58 , T ), U ), Z, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.58 'c_Finite__Set_Osetsum'( Y, T, Z, X ) ), 'c_Finite__Set_Osetsum'( Y, U, Z
% 1.18/1.58 , X ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ), ~(
% 1.18/1.58 'c_Finite__Set_Ofinite'( T, Z ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.58 ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z )
% 1.18/1.58 , U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T )
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y )
% 1.18/1.58 , Z ) ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y )
% 1.18/1.58 , Z ) ), Z ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X )
% 1.18/1.58 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ),
% 1.18/1.58 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X )
% 1.18/1.58 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ),
% 1.18/1.58 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X )
% 1.18/1.58 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ),
% 1.18/1.58 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ) ) ],
% 1.18/1.58 [ =( 'c_Option_Ooption_Ooption__case'( X, Y, hAPP(
% 1.18/1.58 'c_Option_Ooption_OSome'( Z ), T ), U, Z ), hAPP( Y, T ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 1.18/1.58 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_Orderings_Oord__class_Omin'(
% 1.18/1.58 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ),
% 1.18/1.58 'c_HOL_Ominus__class_Ominus'( Y, T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.58 Z, T, X ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ =( 'c_Finite__Set_Ofold'( X, Y, hAPP( hAPP( 'c_Set_Oinsert'( Z ), T )
% 1.18/1.58 , U ), Z, Z ), hAPP( hAPP( X, T ), 'c_Finite__Set_Ofold'( X, Y, U, Z, Z )
% 1.18/1.58 ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ), ~(
% 1.18/1.58 'c_Lattices_Olower__semilattice'( W, V0, X, Z ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.18/1.58 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Finite__Set_Ofun__left__comm'( X, U, W
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ =( X, Y ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( Z, T, U, W,
% 1.18/1.58 V0 ), X ) ) ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( Z, T, U, W,
% 1.18/1.58 V0 ), Y ) ) ), ~( 'c_Finite__Set_Ofun__left__comm'( Z, W, V0 ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.58 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.58 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.58 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.58 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.18/1.58 ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.58 'c_Finite__Set_Osetsum'( Y, Z, T, X ), 'c_Finite__Set_Ofold__image'(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.18/1.58 , T ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~(
% 1.18/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.58 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.18/1.58 ), Z ), Y ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.18/1.58 'c_Finite__Set_Olattice__class_OInf__fin'( X ), 'c_Finite__Set_Ofold1'(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.18/1.58 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( hBOOL( hAPP(
% 1.18/1.58 'c_Finite__Set_Ofold__graph'( Z, T, X, Y, U ), W ) ) ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.18/1.58 'c_OrderedGroup_Oab__semigroup__idem__mult'(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( X ), X ) ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.58 X, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.58 'tc_bool' ) ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Z ), T ) ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.58 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Z ), T ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.58 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.58 , Y ), Z ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.58 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.58 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.58 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.58 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ),
% 1.18/1.58 'c_Complete__Lattice_OInf__class_OInf'( Z, X ) ), 'c_Finite__Set_Ofold'(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y, Z, X, X ) ), ~(
% 1.18/1.58 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.18/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.58 ) ],
% 1.18/1.58 [ =( X, Y ), ~( =( hAPP( 'c_Fun_Ofun__upd'( Z, T, hAPP(
% 1.18/1.58 'c_Option_Ooption_OSome'( U ), X ), W, 'tc_Option_Ooption'( U ) ), T ),
% 1.18/1.58 hAPP( 'c_Option_Ooption_OSome'( U ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.58 ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'(
% 1.18/1.58 X, 'tc_bool' ) ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ),
% 1.18/1.58 'c_Finite__Set_Ofun__left__comm'( 'c_HOL_Otimes__class_Otimes'( X ), X, X
% 1.18/1.58 ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), Z ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), Y ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Z ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.18/1.58 'c_Finite__Set_Ofun__left__comm'( 'c_HOL_Oplus__class_Oplus'( X ), X, X )
% 1.18/1.58 ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_Orderings_Olinorder'(
% 1.18/1.58 'c_COMBC'( 'c_lessequals'( X ), X, X, 'tc_bool' ), 'c_COMBC'(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), X, X, 'tc_bool' ), X ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.18/1.58 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ),
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), Y ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), Z ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Z ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 1.18/1.58 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_Orderings_Oord__class_Omax'(
% 1.18/1.58 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ),
% 1.18/1.58 'c_HOL_Ominus__class_Ominus'( Y, T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.58 Z, T, X ) ) ) ],
% 1.18/1.58 [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP( hAPP( X, W ),
% 1.18/1.58 U ) ) ],
% 1.18/1.58 [ =( hAPP( 'c_COMBK'( X, Y, Z ), T ), X ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Z ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Z ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Z ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_HOL_Oord'( X ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 'tc_fun'( Y, X ) ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'tc_fun'( Y, X ) ), T ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.18/1.58 [ ~( hBOOL( hAPP( X, 'c_Option_Ooption_Ooption__case'( Y, Z,
% 1.18/1.58 'c_Option_Ooption_ONone'( 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X,
% 1.18/1.58 Y ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.18/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.58 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.58 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Z ), hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omin'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( Z,
% 1.18/1.58 'tc_bool' ) ), Y ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 'tc_fun'( Z, 'tc_bool' ) ), X ), Y ) ) ) ],
% 1.18/1.58 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.18/1.58 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ), =(
% 1.18/1.58 Y, X ) ],
% 1.18/1.58 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( Z,
% 1.18/1.58 'tc_bool' ) ), Y ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 'tc_fun'( Z, 'tc_bool' ) ), X ), Y ) ) ) ],
% 1.18/1.58 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), Y ) ) ],
% 1.18/1.58 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.18/1.58 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ), =(
% 1.18/1.58 Y, X ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), =( Z, Y ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 X ), Z ), Y ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Z, Y ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetprod'( Y, hAPP(
% 1.18/1.58 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z,
% 1.18/1.58 'tc_bool' ) ), T ), U ), Z, X ) ), 'c_Finite__Set_Osetprod'( Y, hAPP(
% 1.18/1.58 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z,
% 1.18/1.58 'tc_bool' ) ), T ), U ), Z, X ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetprod'( Y, T, Z, X )
% 1.18/1.58 ), 'c_Finite__Set_Osetprod'( Y, U, Z, X ) ) ), ~(
% 1.18/1.58 'c_Finite__Set_Ofinite'( U, Z ) ), ~( 'c_Finite__Set_Ofinite'( T, Z ) ) ]
% 1.18/1.58 ,
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_lessequals'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ),
% 1.18/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.58 X ), Y ), Z ) ) ) ],
% 1.18/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Orderings_Oord__class_Omax'( X ), Y ), Y ), Y ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.58 , Z ), T ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) )
% 1.18/1.58 ), ~( 'c_Finite__Set_Ofinite'( T, Y ) ), ~( 'c_Finite__Set_Ofinite'( Z,
% 1.18/1.58 Y ) ), =( 'c_Finite__Set_Osetprod'( U, hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.58 , Z ), T ), Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.58 'c_Finite__Set_Osetprod'( U, Z, Y, X ) ), 'c_Finite__Set_Osetprod'( U, T
% 1.18/1.58 , Y, X ) ) ) ],
% 1.18/1.58 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.58 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), Y ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ) ), ~(
% 1.18/1.58 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.18/1.58 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.58 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.58 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ) ), ~(
% 1.18/1.58 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z
% 1.18/1.59 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_HOL_Oord'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( Y, X ) ), Z ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'tc_fun'( Y, X ) ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y
% 1.18/1.59 ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), Y ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), Z ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), Z ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), Z ), Z ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), Z ), Y ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Z ), Y ) ) ) ],
% 1.18/1.59 [ ~( =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ],
% 1.18/1.59 [ ~( =( hAPP( X, 'c_Map_Osko__Map__Xmap__le__def__1__1'( X, Y, Z, T ) )
% 1.18/1.59 , hAPP( Y, 'c_Map_Osko__Map__Xmap__le__def__1__1'( X, Y, Z, T ) ) ) ),
% 1.18/1.59 'c_Map_Omap__le'( X, Y, Z, T ) ],
% 1.18/1.59 [ =( 'c_Option_Ooption_Ooption__case'( X, Y, 'c_Option_Ooption_ONone'( Z
% 1.18/1.59 ), T, Z ), X ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) )
% 1.18/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.18/1.59 , X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.59 'c_Finite__Set_Osetsum'( Y, hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.18/1.59 , T ), U ), Z, X ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y, T, Z, X ) )
% 1.18/1.59 , 'c_Finite__Set_Osetsum'( Y, U, Z, X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.18/1.59 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z,
% 1.18/1.59 'tc_bool' ) ), T ), U ), Z, X ), X ) ), ~( 'c_Finite__Set_Ofinite'( U, Z
% 1.18/1.59 ) ), ~( 'c_Finite__Set_Ofinite'( T, Z ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'(
% 1.18/1.59 X ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'(
% 1.18/1.59 X ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'( X )
% 1.18/1.59 ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z
% 1.18/1.59 ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.59 , X ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.59 ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T
% 1.18/1.59 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), Y
% 1.18/1.59 ) ) ), ~( 'c_Orderings_Olinorder'( T, X, U ) ) ],
% 1.18/1.59 [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( T, Z ), Y
% 1.18/1.59 ) ) ), ~( 'c_Orderings_Olinorder'( T, X, U ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( T, Z ), Y ) ),
% 1.18/1.59 ~( 'c_Orderings_Olinorder'( X, T, U ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Z ), Y ) ),
% 1.18/1.59 ~( 'c_Orderings_Olinorder'( X, T, U ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( T, Z ), Y ) ),
% 1.18/1.59 ~( 'c_Orderings_Olinorder'( T, X, U ) ) ],
% 1.18/1.59 [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( T, Z ), Y
% 1.18/1.59 ) ) ), ~( 'c_Orderings_Olinorder'( X, T, U ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( T, Z ), Y ) ),
% 1.18/1.59 ~( 'c_Orderings_Olinorder'( T, X, U ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), Y ) ), ~( 'c_Orderings_Olinorder'( Z, X, T
% 1.18/1.59 ) ), hBOOL( hAPP( hAPP( Z, Y ), Y ) ) ],
% 1.18/1.59 [ ~( hBOOL( hAPP( hAPP( X, Y ), Y ) ) ), ~( 'c_Orderings_Olinorder'( X,
% 1.18/1.59 Z, T ) ), ~( hBOOL( hAPP( hAPP( Z, Y ), Y ) ) ) ],
% 1.18/1.59 [ =( 'c_Fun_Ofun__upd'( X, Y, hAPP( X, Y ), Z, T ), X ) ],
% 1.18/1.59 [ =( hAPP( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), Y ), Z ) ],
% 1.18/1.59 [ =( 'c_Fun_Ofun__upd'( X, Y, hAPP( X, Y ), Z, T ), X ) ],
% 1.18/1.59 [ =( hAPP( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), Y ), Z ) ],
% 1.18/1.59 [ =( 'c_Fun_Ofun__upd'( X, Y, hAPP( X, Y ), Z, T ), X ) ],
% 1.18/1.59 [ 'c_OrderedGroup_Oab__semigroup__idem__mult'( X, Y ), ~(
% 1.18/1.59 'c_Lattices_Olower__semilattice'( Z, T, X, Y ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( X, T ), U ) ) ), ~( 'c_Lattices_Olower__semilattice'( W, X, Y, V0 )
% 1.18/1.59 ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( X, Z ), U ) ) ), ~( 'c_Lattices_Olower__semilattice'( W, X, Y, V0 )
% 1.18/1.59 ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.18/1.59 hAPP( T, U ), Z ) ) ) ), ~( 'c_Lattices_Olower__semilattice'( X, W, T, V0
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.18/1.59 hAPP( T, Z ), U ) ) ) ), ~( 'c_Lattices_Olower__semilattice'( X, W, T, V0
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.18/1.59 hAPP( T, Z ), U ) ) ) ), ~( 'c_Lattices_Olower__semilattice'( X, W, T, V0
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.18/1.59 hAPP( T, U ), Z ) ) ) ), ~( 'c_Lattices_Olower__semilattice'( X, W, T, V0
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( X, Z ), U ) ) ), ~( 'c_Lattices_Olower__semilattice'( X, W, Y, V0 )
% 1.18/1.59 ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( X, T ), U ) ) ), ~( 'c_Lattices_Olower__semilattice'( X, W, Y, V0 )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.18/1.59 'c_Lattices_Olower__semilattice'( 'c_COMBC'( 'c_lessequals'( X ), X, X,
% 1.18/1.59 'tc_bool' ), 'c_COMBC'( 'c_HOL_Oord__class_Oless'( X ), X, X, 'tc_bool' )
% 1.18/1.59 , 'c_Orderings_Oord__class_Omax'( X ), X ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), U ) ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z )
% 1.18/1.59 , U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , T ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ),
% 1.18/1.59 Z ) ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ),
% 1.18/1.59 Z ) ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), Z ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), Y ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), Z ) ), Y ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), Z ) ), Z ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 , Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 , Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.59 ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), Y ) ],
% 1.18/1.59 [ ~( hBOOL( hAPP( hAPP( X, Y ), Y ) ) ), ~( 'c_Orderings_Olinorder'( Z,
% 1.18/1.59 X, T ) ) ],
% 1.18/1.59 [ ~( 'c_Orderings_Olinorder'( X, Y, Z ) ), ~( hBOOL( hAPP( hAPP( Y, T )
% 1.18/1.59 , T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_SetInterval_Oord__class_OlessThan'( Y, X ) ),
% 1.18/1.59 'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OlessThan'( Y, X )
% 1.18/1.59 ), 'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.18/1.59 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.18/1.59 Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( X, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) ) ), ~(
% 1.18/1.59 'c_Lattices_Olower__semilattice'( X, W, Z, V0 ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~(
% 1.18/1.59 'c_Lattices_Olower__semilattice'( X, U, Y, W ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~(
% 1.18/1.59 'c_Lattices_Olower__semilattice'( X, U, Y, W ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( X, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) ) ), ~(
% 1.18/1.59 'c_Lattices_Olower__semilattice'( X, W, Z, V0 ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( X, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) ) ), ~(
% 1.18/1.59 'c_Lattices_Olower__semilattice'( X, W, Z, V0 ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), Z ), Y ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), Z ), Z ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Z ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Y ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Y ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Z ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), Y ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Z ), Y ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), Z ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.18/1.59 Z ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.18/1.59 Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), T ), Y ) ), Z ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Z ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), Y ) ) ],
% 1.18/1.59 [ 'c_Complete__Lattice_Ocomplete__lattice'( X, Y, 'c_COMBC'( Z, T, T,
% 1.18/1.59 'tc_bool' ), 'c_COMBC'( U, T, T, 'tc_bool' ), W, V0, V1, V2, T ), ~(
% 1.18/1.59 'c_Complete__Lattice_Ocomplete__lattice'( Y, X, Z, U, V0, W, V2, V1, T )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Z ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.18/1.59 'c_SetInterval_Oord__class_OlessThan'( Y, X ),
% 1.18/1.59 'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ),
% 1.18/1.59 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ), Y ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ) ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), T ), Y ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ) ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), T ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.59 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.59 ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.59 [ =( 'c_Fun_Ofun__upd'( 'c_Map_Orestrict__map'( X, Y, Z, T ), U,
% 1.18/1.59 'c_Option_Ooption_ONone'( T ), Z, 'tc_Option_Ooption'( T ) ),
% 1.18/1.59 'c_Map_Orestrict__map'( X, Y, Z, T ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), U
% 1.18/1.59 ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), T ), Z ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ),
% 1.18/1.59 'c_SetInterval_Oord__class_OatLeastAtMost'( T, U, X ) ),
% 1.18/1.59 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), T ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Z ), U ), X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.18/1.59 [ =( 'c_Finite__Set_Ofold'( X, Y, Z, T, U ), W ), ~( hBOOL( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold__graph'( X, Y, Z, T, U ), W ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofun__left__comm'( X, T, U ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'( X )
% 1.18/1.59 ), Y ) ), =( 'c_Suc'( X ), Y ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.59 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_Set_Ovimage'( Y, Z, X, T ) ), 'c_Set_Ovimage'( Y, U, X, T ) ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( T, 'tc_bool' ) ), Z ), U ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.18/1.59 'c_Lattices_Olower__semilattice'( 'c_COMBC'( 'c_lessequals'( X ), X, X,
% 1.18/1.59 'tc_bool' ), 'c_COMBC'( 'c_HOL_Oord__class_Oless'( X ), X, X, 'tc_bool' )
% 1.18/1.59 , 'c_Lattices_Oupper__semilattice__class_Osup'( X ), X ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z
% 1.18/1.59 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y
% 1.18/1.59 ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X
% 1.18/1.59 , 'tc_bool' ) ), T ), Z ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z
% 1.18/1.59 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y
% 1.18/1.59 ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X
% 1.18/1.59 , 'tc_bool' ) ), Z ), T ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.59 ), Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z
% 1.18/1.59 ), T ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.59 ), Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), T
% 1.18/1.59 ), Z ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.59 ), Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z
% 1.18/1.59 ), T ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.59 ), Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), T
% 1.18/1.59 ), Z ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), 'c_Finite__Set_Ofold'(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y, Z, X, X ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), T ), Y ) ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Z ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Y,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.18/1.59 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.18/1.59 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), ~( =( hAPP( Y, Z ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Z
% 1.18/1.59 ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ), =(
% 1.18/1.59 'c_Finite__Set_Osetprod'( Y, U, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), ~( =( hAPP( Y,
% 1.18/1.59 Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T
% 1.18/1.59 ), Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ), =(
% 1.18/1.59 'c_Finite__Set_Osetprod'( Y, U, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Z ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), T ), U ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), U ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_SetInterval_Oord__class_OatLeastAtMost'( U, Y, X ) ),
% 1.18/1.59 'c_SetInterval_Oord__class_OatLeastAtMost'( T, Z, X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ),
% 1.18/1.59 hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Y ), T ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 , Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 , Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.59 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 , Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.59 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.59 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.18/1.59 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.18/1.59 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ),
% 1.18/1.59 'c_Complete__Lattice_OSup__class_OSup'( Z, X ) ), 'c_Finite__Set_Ofold'(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y, Z, X, X ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Y ), Y ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), Y ), Y ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.59 ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), T ), Y
% 1.18/1.59 ) ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.59 ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T
% 1.18/1.59 ) ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.59 ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), T ), Y
% 1.18/1.59 ) ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.59 ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T
% 1.18/1.59 ) ), Z ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z
% 1.18/1.59 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), T ) ), Z ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z
% 1.18/1.59 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), T ), Y ) ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( 't_a', X ) ), Y )
% 1.18/1.59 , Z ), 'v_x' ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.59 X ), hAPP( Y, 'v_x' ) ), hAPP( Z, 'v_x' ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), T ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.59 ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) )
% 1.18/1.59 ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Y
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Y
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z
% 1.18/1.59 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), T
% 1.18/1.59 ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.59 ) ), Y ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( Z, Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( 'tc_fun'( T, 'tc_bool' ) ), Z ), X ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), Y ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Y ) ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( Y, 'tc_bool' ) ), X ),
% 1.18/1.59 Z ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.59 ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.59 ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'(
% 1.18/1.59 Z, 'tc_bool' ) ), T ), X ) ) ), ~( hBOOL( hAPP( T, Y ) ) ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( Y, 'tc_bool' ) ), X ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z,
% 1.18/1.59 Y ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.59 ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), U ), T ) ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( T
% 1.18/1.59 , U, X ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.18/1.59 'c_OrderedGroup_Oab__semigroup__idem__mult'(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), X ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , T ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) )
% 1.18/1.59 ],
% 1.18/1.59 [ =( hAPP( 'c_Fun_Ofun__upd'( X, Y, hAPP( 'c_Option_Ooption_OSome'( Z )
% 1.18/1.59 , T ), U, 'tc_Option_Ooption'( Z ) ), Y ), hAPP( 'c_Option_Ooption_OSome'(
% 1.18/1.59 Z ), T ) ) ],
% 1.18/1.59 [ ~( =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ), T ) ) ), =(
% 1.18/1.59 'c_Fun_Ofun__upd'( X, Y, hAPP( 'c_Option_Ooption_OSome'( Z ), T ), U,
% 1.18/1.59 'tc_Option_Ooption'( Z ) ), X ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'( X )
% 1.18/1.59 ), Y ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'(
% 1.18/1.59 Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X )
% 1.18/1.59 , Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) )
% 1.18/1.59 ), ~( 'c_Finite__Set_Ofinite'( T, Y ) ), ~( 'c_Finite__Set_Ofinite'( Z,
% 1.18/1.59 Y ) ), =( 'c_Finite__Set_Ofold__image'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.59 U, 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ), X, Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.59 'c_Finite__Set_Ofold__image'( 'c_HOL_Oplus__class_Oplus'( X ), U,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X, Y ) ),
% 1.18/1.59 'c_Finite__Set_Ofold__image'( 'c_HOL_Oplus__class_Oplus'( X ), U,
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X, Y ) ) ) ],
% 1.18/1.59 [ =( X, Y ), hBOOL( hAPP( hAPP( Z, Y ), X ) ), hBOOL( hAPP( hAPP( Z, X )
% 1.18/1.59 , Y ) ), ~( 'c_Orderings_Olinorder'( T, Z, U ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Z ), Y ) ),
% 1.18/1.59 =( Z, Y ), ~( 'c_Orderings_Olinorder'( T, X, U ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), =( Z, Y ), hBOOL( hAPP( hAPP( X, Z )
% 1.18/1.59 , Y ) ), ~( 'c_Orderings_Olinorder'( T, X, U ) ) ],
% 1.18/1.59 [ =( X, Y ), hBOOL( hAPP( hAPP( Z, X ), Y ) ), hBOOL( hAPP( hAPP( Z, Y )
% 1.18/1.59 , X ) ), ~( 'c_Orderings_Olinorder'( T, Z, U ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), T ) ), ~( hBOOL( hAPP( Z, T ) ) ),
% 1.18/1.59 ~( hBOOL( hAPP( Y, T ) ) ) ],
% 1.18/1.59 [ =( hAPP( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), W ), hAPP( X, W ) ), =( W
% 1.18/1.59 , Y ) ],
% 1.18/1.59 [ =( hAPP( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), W ), hAPP( X, W ) ), =( W
% 1.18/1.59 , Y ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y )
% 1.18/1.59 , hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Orderings_Oord__class_Omin'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), X ), Y ) ), hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold1'( 'c_Orderings_Oord__class_Omin'( X ), X ), Z ) ) )
% 1.18/1.59 , ~( 'c_Finite__Set_Ofinite'( Y, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Z ), Y ) ) ), =( Z,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.18/1.59 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), Z ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( 'tc_fun'( T, 'tc_bool' ) ), X ), Y ) ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( T, 'tc_bool' ) ), Z ), X ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.18/1.59 , U, X ) ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), U ), T ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.18/1.59 , U, X ) ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), Y ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), U ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.18/1.59 , U, X ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), U )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.18/1.59 , U, X ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), U ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , 'c_SetInterval_Oord__class_OlessThan'( Y, X ) ),
% 1.18/1.59 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofun__left__comm'( X, Y, Y ), ~(
% 1.18/1.59 'c_OrderedGroup_Oab__semigroup__mult'( X, Y ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ) ), =( Z, Y ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.59 ), Y ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ =( X, Y ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( Z,
% 1.18/1.59 'tc_bool' ) ), X ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'(
% 1.18/1.59 Z, 'tc_bool' ) ), X ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( =( 'c_Fun_Ofun__upd'( X, Y, hAPP( 'c_Option_Ooption_OSome'( Z ), T
% 1.18/1.59 ), U, 'tc_Option_Ooption'( Z ) ), 'c_Fun_Ofun__upd'( W, Y, hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( Z ), V0 ), U, 'tc_Option_Ooption'( Z ) ) ) ),
% 1.18/1.59 =( T, V0 ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ),
% 1.18/1.59 'c_SetInterval_Oord__class_OatLeastAtMost'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.59 ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), T ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.18/1.59 ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Z ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.18/1.59 ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Z ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.59 ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), X ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'( X
% 1.18/1.59 ) ) ) ],
% 1.18/1.59 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y )
% 1.18/1.59 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ),
% 1.18/1.59 'c_Suc'( X ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'(
% 1.18/1.59 Y ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), T ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.18/1.59 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), T ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.18/1.59 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.59 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ =( X, Y ), hBOOL( hAPP( hAPP( Z, X ), Y ) ), ~( hBOOL( hAPP( hAPP( T,
% 1.18/1.59 X ), Y ) ) ), ~( 'c_Orderings_Olinorder'( T, Z, U ) ) ],
% 1.18/1.59 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, X ), Y ) ) ), hBOOL( hAPP( hAPP( T
% 1.18/1.59 , X ), Y ) ), ~( 'c_Orderings_Olinorder'( Z, T, U ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.59 X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.18/1.59 , T ), X ), Y ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.18/1.59 , X ), T ), Y ) ) ) ],
% 1.18/1.59 [ ~( =( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), X ) ), =( hAPP( X, Y ), Z )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.18/1.59 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.18/1.59 Y ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.18/1.59 Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.18/1.59 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 Y ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.18/1.59 Y ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.18/1.59 Y ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.59 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 , Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 , Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 , Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.59 , Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.59 , Y ), Z ), Z, X ), Y ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.59 ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, X ) ),
% 1.18/1.59 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, U, X ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Y ) ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.59 ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( T, Y, X ) ),
% 1.18/1.59 'c_SetInterval_Oord__class_OatLeastAtMost'( U, Z, X ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, 'c_Finite__Set_Ofold'( Y, Z, T, U, U ) ), hAPP(
% 1.18/1.59 hAPP( Y, W ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), T ) ) ),
% 1.18/1.59 ~( 'c_Finite__Set_Ofinite'( T, U ) ), ~( 'c_Lattices_Olower__semilattice'(
% 1.18/1.59 X, V0, Y, U ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( X, Y ), 'c_Finite__Set_Ofold'( X, Z, T, U, W ) ),
% 1.18/1.59 'c_Finite__Set_Ofold'( X, hAPP( hAPP( X, Y ), Z ), T, U, W ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( T, U ) ), ~( 'c_Finite__Set_Ofun__left__comm'( X
% 1.18/1.59 , U, W ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ =( 'c_Set_Ovimage'( X, hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ), U, Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( U, 'tc_bool' ) )
% 1.18/1.59 , 'c_Set_Ovimage'( X, Z, U, Y ) ), 'c_Set_Ovimage'( X, T, U, Y ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'( X )
% 1.18/1.59 ), 'c_Suc'( Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'tc_nat' ), X ), Y ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'( X )
% 1.18/1.59 ), 'c_Suc'( Y ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'( X )
% 1.18/1.59 ), 'c_Suc'( Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'tc_nat' ), X ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 X ), Y ), Y ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.59 Y ) ) ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_HOL_Oord'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.59 hAPP( Y, Z ) ), hAPP( T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( U, X ) ), Y ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), T ), Z ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), T ), Z ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), T ), Z ) ) ) ],
% 1.18/1.59 [ =( hAPP( 'c_Map_Orestrict__map'( X, Y, Z, T ), U ), hAPP( X, U ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), Y ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), T ), Z ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , T ), Z ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ) ) ) ) ],
% 1.18/1.59 [ ~( =( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool' ),
% 1.18/1.59 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool'
% 1.18/1.59 ), 'tc_bool' ), Z ) ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), hBOOL( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold__graph'( 'c_HOL_Otimes__class_Otimes'( X ), Y, hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Z ), T ), X, X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Z ), T ) ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z, T, X, X ), U ) ) ) ],
% 1.18/1.59 [ ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y, Z, T, U ), W ) ) )
% 1.18/1.59 , hBOOL( hAPP( hAPP( 'c_in'( T ), V0 ), Z ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofun__left__comm'( X, T, U ) ), hBOOL( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold__graph'( X, Y, hAPP( hAPP( 'c_Set_Oinsert'( T ), V0
% 1.18/1.59 ), Z ), T, U ), hAPP( hAPP( X, V0 ), W ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.59 ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_in'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.59 ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_in'( X ), Z ), Y ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z )
% 1.18/1.59 , T ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z
% 1.18/1.59 ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Y ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), T ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), Z
% 1.18/1.59 ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold__graph'( 'c_HOL_Oplus__class_Oplus'( X ), Y, hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Z ), T ), X, X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), U ) ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.18/1.59 X ), Z ), T ) ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ), U ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( X ) ), Y ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( X ) ), 'c_Orderings_Obot__class_Obot'( X
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Obot'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.59 ), 'c_Orderings_Obot__class_Obot'( X ) ), Y ) ) ],
% 1.18/1.59 [ =( 'c_Finite__Set_Ofold__image'( X, Y, Z,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), U, T ), Z ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( 'c_Finite__Set_Ofold'( X, Y, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), Y ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.18/1.59 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( Y, 'tc_bool' ) ), X ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ) ) ],
% 1.18/1.59 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ) ) ) ],
% 1.18/1.59 [ =( X, Y ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( Z, Y,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T, U ), X ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.59 ) ) ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.18/1.59 ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), Y ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), Y ) )
% 1.18/1.59 ],
% 1.18/1.59 [ 'c_Nitpick_Ofold__graph_H'( X, Y, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( Z, 'tc_bool' ) ), Y, Z, T ) ],
% 1.18/1.59 [ =( hAPP( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.59 'tc_fun'( 't_a', 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a',
% 1.18/1.59 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool' ), X ) ), hAPP( 'c_COMBC'( 'c_in'(
% 1.18/1.59 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool' ), Y ) ), 'v_x' )
% 1.18/1.59 , hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( 't_a', 'tc_bool'
% 1.18/1.59 ) ), X ), Y ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.59 , Y ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Z ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), Y ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Y ), T ) ), hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.59 , Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Z ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z
% 1.18/1.59 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), Y ) ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), 'c_Complete__Lattice_OSup__class_OSup'( Z
% 1.18/1.59 , X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.59 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.59 Z ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.59 'c_Finite__Set_Ofold__image'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( T ), U ), W ), X, T ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, U ) ),
% 1.18/1.59 'c_Finite__Set_Ofold__image'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, W, X
% 1.18/1.59 , T ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), U ), W ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( W, T ) ) ],
% 1.18/1.59 [ =( 'c_Finite__Set_Ofold'( X, Y, hAPP( hAPP( 'c_Set_Oinsert'( Z ), T )
% 1.18/1.59 , U ), Z, W ), 'c_Finite__Set_Ofold'( X, hAPP( hAPP( X, T ), Y ), U, Z, W
% 1.18/1.59 ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( U, Z ) ), ~( 'c_Finite__Set_Ofun__left__comm'( X
% 1.18/1.59 , Z, W ) ) ],
% 1.18/1.59 [ =( 'c_Finite__Set_Ofold'( X, Y, hAPP( hAPP( 'c_Set_Oinsert'( Z ), T )
% 1.18/1.59 , U ), Z, W ), hAPP( hAPP( X, T ), 'c_Finite__Set_Ofold'( X, Y, U, Z, W )
% 1.18/1.59 ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( U, Z ) ), ~( 'c_Finite__Set_Ofun__left__comm'( X
% 1.18/1.59 , Z, W ) ) ],
% 1.18/1.59 [ =( 'c_Finite__Set_Ocard'( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ),
% 1.18/1.59 X ), 'c_Suc'( 'c_Finite__Set_Ocard'( Z, X ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Y ), Z ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.59 'c_Finite__Set_Osetsum'( Y, hAPP( hAPP( 'c_Set_Oinsert'( Z ), T ), U ), Z
% 1.18/1.59 , X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, T ) ),
% 1.18/1.59 'c_Finite__Set_Osetsum'( Y, U, Z, X ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.18/1.59 , T ), U ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.18/1.59 'c_Finite__Set_Ofold__image'( 'c_HOL_Otimes__class_Otimes'( X ), Y, Z,
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( T ), U ), W ), X, T ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, U ) ),
% 1.18/1.59 'c_Finite__Set_Ofold__image'( 'c_HOL_Otimes__class_Otimes'( X ), Y, Z, W
% 1.18/1.59 , X, T ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), U ), W ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( W, T ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.18/1.59 'c_Finite__Set_Osetprod'( Y, hAPP( hAPP( 'c_Set_Oinsert'( Z ), T ), U ),
% 1.18/1.59 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, T ) ),
% 1.18/1.59 'c_Finite__Set_Osetprod'( Y, U, Z, X ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z
% 1.18/1.59 ), T ), U ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ),
% 1.18/1.59 'c_Finite__Set_Ofold'( 'c_Lattices_Oupper__semilattice__class_Osup'( X )
% 1.18/1.59 , Z, T, X, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( T, X ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ) ), =( 'c_Finite__Set_Ocard'( hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ), X ), 'c_Suc'( 'c_Finite__Set_Ocard'(
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.18/1.59 'c_Complete__Lattice_OSup__class_OSup'( Y, X ), 'c_Finite__Set_Ofold'(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( X ), Y, X, X ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.59 'c_Finite__Set_Osetsum'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'(
% 1.18/1.59 U, 'tc_bool' ) ), U, X ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.59 'c_Finite__Set_Osetsum'( Y, Z, U, X ), 'c_Finite__Set_Osetsum'( Y, T, U,
% 1.18/1.59 X ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( U, 'tc_bool'
% 1.18/1.59 ) ), T ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, U ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.59 ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.18/1.59 , 'tc_bool' ) ) ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( 'c_Fun_Ofun__upd'( 'c_Map_Orestrict__map'( X, Y, Z, T ), U, W, Z,
% 1.18/1.59 'tc_Option_Ooption'( T ) ), 'c_Fun_Ofun__upd'( 'c_Map_Orestrict__map'( X
% 1.18/1.59 , 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP( 'c_Set_Oinsert'( Z ), U )
% 1.18/1.59 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ), 'tc_fun'(
% 1.18/1.59 Z, 'tc_bool' ) ), Z, T ), U, W, Z, 'tc_Option_Ooption'( T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( X ), X ), Y ) ), Z ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ), ~( 'c_Finite__Set_Ofinite'(
% 1.18/1.59 Y, X ) ) ],
% 1.18/1.59 [ =( hAPP( 'c_Finite__Set_Ofold1'( X, Y ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 Y ), Z ), T ) ), 'c_Finite__Set_Ofold'( X, Z, T, Y, Y ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( T, Y ) ), ~(
% 1.18/1.59 'c_OrderedGroup_Oab__semigroup__idem__mult'( X, Y ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X ), hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), 'c_Finite__Set_Ofold'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y, Z, X, X ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMax'( X ), Y ), Z ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.59 ), 'c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1'(
% 1.18/1.59 Y, Z, X ) ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMin'( X ), Y ), Z ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.59 ), Z ),
% 1.18/1.59 'c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1'( Y,
% 1.18/1.59 Z, X ) ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( 'c_Finite__Set_Olinorder__class_OMax'( X ), Y
% 1.18/1.59 ) ), hAPP( 'c_Finite__Set_Olinorder__class_OMax'( X ), Z ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( 'c_Finite__Set_Olinorder__class_OMin'( X ), Y
% 1.18/1.59 ) ), hAPP( 'c_Finite__Set_Olinorder__class_OMin'( X ), Z ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, X ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Z ), Y ) ) ) ],
% 1.18/1.59 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Y ), T ) ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , T ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.18/1.59 ) ],
% 1.18/1.59 [ hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( Z ), T ), U ), Z, W ), hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.18/1.59 hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y, U, Z, W ), V0 ) ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Z ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z
% 1.18/1.59 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y
% 1.18/1.59 ), hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), Z ) ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), T ), Y ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( X ), Z ), Y ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z
% 1.18/1.59 ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( X ), T ), Z ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( X ), Z ), Y ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 X ), Y ), T ) ), Z ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.59 ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Z ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), Z ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.59 ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.18/1.59 'c_Complete__Lattice_OSup__class_OSup'( 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), X ), 'c_Orderings_Obot__class_Obot'( X ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.18/1.59 'c_Complete__Lattice_OSup__class_OSup'( hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.59 , Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), X )
% 1.18/1.59 , Y ) ],
% 1.18/1.59 [ =( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ), =( X,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( 'tc_fun'( Y, 'tc_bool' ) ), X ), hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.18/1.59 'tc_bool' ) ) ) ) ) ) ],
% 1.18/1.59 [ =( 'c_Fun_Ofun__upd'( 'c_Map_Orestrict__map'( X, Y, Z, T ), U, W, Z,
% 1.18/1.59 'tc_Option_Ooption'( T ) ), 'c_Fun_Ofun__upd'( 'c_Map_Orestrict__map'( X
% 1.18/1.59 , 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP( 'c_Set_Oinsert'( Z ), U )
% 1.18/1.59 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ), 'tc_fun'(
% 1.18/1.59 Z, 'tc_bool' ) ), Z, T ), U, W, Z, 'tc_Option_Ooption'( T ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_in'( Z ), U ), Y ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.59 ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.18/1.59 , 'tc_bool' ) ) ), T ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), T ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold__graph'( 'c_HOL_Oplus__class_Oplus'( X ), Y, hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Z ), 'c_HOL_Ominus__class_Ominus'( T, hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_bool' ) ) ), X, X ), U ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_in'( X ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y
% 1.18/1.59 ), T ) ) ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ), U ) ) ) ],
% 1.18/1.59 [ =( 'c_Map_Orestrict__map'( 'c_Fun_Ofun__upd'( X, Y, Z, T,
% 1.18/1.59 'tc_Option_Ooption'( U ) ), W, T, U ), 'c_Fun_Ofun__upd'(
% 1.18/1.59 'c_Map_Orestrict__map'( X, 'c_HOL_Ominus__class_Ominus'( W, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( T ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.18/1.59 'tc_bool' ) ) ), 'tc_fun'( T, 'tc_bool' ) ), T, U ), Y, Z, T,
% 1.18/1.59 'tc_Option_Ooption'( U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), W )
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), hBOOL( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold__graph'( 'c_HOL_Otimes__class_Otimes'( X ), Y, hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Z ), 'c_HOL_Ominus__class_Ominus'( T, hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_bool' ) ) ), X, X ), U ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_in'( X ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y
% 1.18/1.59 ), T ) ) ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z, T, X, X ), U ) ) ) ],
% 1.18/1.59 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.18/1.59 'c_Complete__Lattice_OSup__class_OSup'( hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.59 , Y ), Z ), X ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.59 X ), Y ), 'c_Complete__Lattice_OSup__class_OSup'( Z, X ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.18/1.59 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), =( 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Y
% 1.18/1.59 , Z, X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.18/1.59 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.18/1.59 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ =( 'c_Finite__Set_Ofold'( X, Y, hAPP( hAPP( 'c_Set_Oinsert'( Z ), T )
% 1.18/1.59 , U ), Z, W ), hAPP( hAPP( X, T ), 'c_Finite__Set_Ofold'( X, Y,
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( U, hAPP( hAPP( 'c_Set_Oinsert'( Z ), T ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ), 'tc_fun'( Z
% 1.18/1.59 , 'tc_bool' ) ), Z, W ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofun__left__comm'( X, Z, W ) ) ],
% 1.18/1.59 [ =( 'c_Finite__Set_Ocard'( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ),
% 1.18/1.59 X ), 'c_Suc'( 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'( Z,
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_bool' ) ), X ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), X ), Y ) ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X
% 1.18/1.59 ), T ), Y ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.18/1.59 X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.59 Y ), hAPP( 'c_Finite__Set_Ofold1'( 'c_Orderings_Oord__class_Omin'( X ), X
% 1.18/1.59 ), T ) ) ) ), =( T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), X ), Y ) ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), T ), Y ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ),
% 1.18/1.59 T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold1'( 'c_Lattices_Olower__semilattice__class_Oinf'( X )
% 1.18/1.59 , X ), T ) ) ) ), =( T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( T, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X ), hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), 'c_Finite__Set_Ofold'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y, Z, X, X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Y ), Z ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold1'( 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( X ), Y ), Z ) ), 'c_Finite__Set_Ofold'(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Y ), Z ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.59 [ =( X, hAPP( 'c_Option_Ooption_OSome'( Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( Y ), Z ), 'c_Option_Oset'( X, Y ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Option_Oset'( hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( X ), Y ), X ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ ~( =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ) ],
% 1.18/1.59 [ =( hAPP( 'c_Map_Orestrict__map'( X, Y, Z, T ), U ),
% 1.18/1.59 'c_Option_Ooption_ONone'( T ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), Y )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.18/1.59 ), =( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.59 ~( 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, X ) ), =( hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold1'( 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ) ), hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold1'( 'c_HOL_Oplus__class_Oplus'( X ), X ), Z ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.18/1.59 ), =( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.59 ~( 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, X ) ), =( hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X ), Y ) ),
% 1.18/1.59 hAPP( 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X ), Z )
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ) ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ), T ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Z ), T ) ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ), Z ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), Z ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ), Y ) ],
% 1.18/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.59 , 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Y, 'tc_bool' ) ) ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.59 , 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Y, 'tc_bool' ) ) ) ) ],
% 1.18/1.59 [ =( 'c_Option_Oset'( 'c_Option_Ooption_ONone'( X ), X ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ ~( =( 'c_Option_Oset'( X, Y ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( Y, 'tc_bool' ) ) ) ), =( X, 'c_Option_Ooption_ONone'( Y ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( X ), 'c_Complete__Lattice_OInf__class_OInf'( Y, X )
% 1.18/1.59 ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( X, Y ), hAPP( Z, T ) ), 'c_Finite__Set_Ofold'( X, Y, T
% 1.18/1.59 , U, U ) ), ~( 'c_Finite__Set_Ofinite'( T, U ) ), ~(
% 1.18/1.59 'c_Complete__Lattice_Ocomplete__lattice'( W, Z, V0, V1, V2, X, V3, V4, U
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( X, Y ), hAPP( Z, T ) ), 'c_Finite__Set_Ofold'( X, Y, T
% 1.18/1.59 , U, U ) ), ~( 'c_Finite__Set_Ofinite'( T, U ) ), ~(
% 1.18/1.59 'c_Complete__Lattice_Ocomplete__lattice'( Z, W, V0, V1, X, V2, V3, V4, U
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ =( hAPP( X, Y ), 'c_Finite__Set_Ofold'( Z, T, Y, U, U ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, U ) ), ~(
% 1.18/1.59 'c_Complete__Lattice_Ocomplete__lattice'( W, X, V0, V1, V2, Z, T, V3, U )
% 1.18/1.59 ) ],
% 1.18/1.59 [ =( hAPP( X, Y ), 'c_Finite__Set_Ofold'( Z, T, Y, U, U ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, U ) ), ~(
% 1.18/1.59 'c_Complete__Lattice_Ocomplete__lattice'( X, W, V0, V1, Z, V2, V3, T, U )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.18/1.59 'c_Complete__Lattice_OInf__class_OInf'( hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.59 , Y ), Z ), X ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.59 X ), Y ), 'c_Complete__Lattice_OInf__class_OInf'( Z, X ) ) ) ],
% 1.18/1.59 [ =( 'c_Map_Omap__add'( X, 'c_Fun_Ofun__upd'( Y, Z, hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( T ), U ), W, 'tc_Option_Ooption'( T ) ), W, T )
% 1.18/1.59 , 'c_Fun_Ofun__upd'( 'c_Map_Omap__add'( X, Y, W, T ), Z, hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( T ), U ), W, 'tc_Option_Ooption'( T ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( 'c_Map_Omap__add'( 'c_COMBK'( 'c_Option_Ooption_ONone'( X ),
% 1.18/1.59 'tc_Option_Ooption'( X ), Y ), Z, Y, X ), Z ) ],
% 1.18/1.59 [ =( 'c_Map_Omap__add'( X, 'c_COMBK'( 'c_Option_Ooption_ONone'( Y ),
% 1.18/1.59 'tc_Option_Ooption'( Y ), Z ), Z, Y ), X ) ],
% 1.18/1.59 [ 'c_Map_Omap__le'( 'c_Fun_Ofun__upd'( X, Y, 'c_Option_Ooption_ONone'( Z
% 1.18/1.59 ), T, 'tc_Option_Ooption'( Z ) ), X, T, Z ) ],
% 1.18/1.59 [ 'c_Map_Omap__le'( 'c_COMBK'( 'c_Option_Ooption_ONone'( X ),
% 1.18/1.59 'tc_Option_Ooption'( X ), Y ), Z, Y, X ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_Map_Odom'( Y, X, Z ) ), 'c_Map_Odom'( T, X, Z ) ) ), ~(
% 1.18/1.59 'c_Map_Omap__le'( Y, T, X, Z ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMax'( X ), 'c_Finite__Set_Ofold1'(
% 1.18/1.59 'c_Orderings_Oord__class_Omax'( X ), X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMin'( X ), 'c_Finite__Set_Ofold1'(
% 1.18/1.59 'c_Orderings_Oord__class_Omin'( X ), X ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ), X ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), X ) ],
% 1.18/1.59 [ ~( =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ ~( =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ =( 'c_Set_Ovimage'( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), T ), U,
% 1.18/1.59 Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 U, 'tc_bool' ) ), 'c_Set_Ovimage'( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z
% 1.18/1.59 ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), U, Y )
% 1.18/1.59 ), 'c_Set_Ovimage'( X, T, U, Y ) ) ) ],
% 1.18/1.59 [ =( hAPP( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 U, Z ), hAPP( X, T ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X
% 1.18/1.59 , W, V0, V1, U, V2, V3, V4, Y ) ) ],
% 1.18/1.59 [ =( hAPP( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 U, Z ), hAPP( X, T ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W
% 1.18/1.59 , X, V0, V1, V2, U, V3, V4, Y ) ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ), X
% 1.18/1.59 ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'( hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( Y ), Z ), X ), Y ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), T ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ) ) ) ],
% 1.18/1.59 [ ~( =( hAPP( X, Y ), 'c_Option_Ooption_ONone'( Z ) ) ), =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( 'c_Map_Odom'( X, T, Z ), hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( T ), Y ), U ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( 'c_Map_Odom'( X, T, Z ), U, 'tc_fun'( T,
% 1.18/1.59 'tc_bool' ) ) ) ],
% 1.18/1.59 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSemi'( Y, Z ) ) ) ],
% 1.18/1.59 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OBODY'( Z ) ) ) ],
% 1.18/1.59 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OSemi'( X, Y ) ) ) ],
% 1.18/1.59 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ],
% 1.18/1.59 [ 'c_Hoare__Mirabelle_Ohoare__valids'( X, Y, Z ), ~(
% 1.18/1.59 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSemi'( X, Y ) ), Z
% 1.18/1.59 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( Y ), U ), T ) ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( X ), Z ), U ) ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y )
% 1.18/1.59 , Z ), T, 'tc_fun'( X, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Z, T
% 1.18/1.59 , 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T
% 1.18/1.59 ) ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y )
% 1.18/1.59 , Z ), T, 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y
% 1.18/1.59 ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ],
% 1.18/1.59 [ =( hAPP( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ), Z ), ~(
% 1.18/1.59 'c_Complete__Lattice_Ocomplete__lattice'( X, T, U, W, V0, V1, V2, V3, Y )
% 1.18/1.59 ) ],
% 1.18/1.59 [ =( hAPP( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ), Z ), ~(
% 1.18/1.59 'c_Complete__Lattice_Ocomplete__lattice'( T, X, U, W, V0, V1, V2, V3, Y )
% 1.18/1.59 ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.59 'c_Nitpick_Osko__Nitpick__XEx1__def__1__3'( hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 X ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), X
% 1.18/1.59 ) ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( 'c_Finite__Set_Osetsum'(
% 1.18/1.59 Y, 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_Set_Oinsert'( T ), U )
% 1.18/1.59 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ), 'tc_fun'(
% 1.18/1.59 T, 'tc_bool' ) ), T, X ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.59 'c_Finite__Set_Osetsum'( Y, Z, T, X ), hAPP( Y, U ), X ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_in'( T ), U ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, T )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.59 'c_Finite__Set_Osetsum'( Y, 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( T ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.18/1.59 'tc_bool' ) ) ), 'tc_fun'( T, 'tc_bool' ) ), T, X ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( 'c_Finite__Set_Osetsum'( Y, Z, T, X ), hAPP(
% 1.18/1.59 Y, U ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), U ), Z ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Z, T ) ) ],
% 1.18/1.59 [ ~( =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y
% 1.18/1.59 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, X ) ), ~(
% 1.18/1.59 'c_OrderedGroup_Oab__semigroup__mult'( T, X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold1'( T, X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ) ), hAPP( hAPP( T, hAPP( 'c_Finite__Set_Ofold1'( T, X ), Y ) )
% 1.18/1.59 , hAPP( 'c_Finite__Set_Ofold1'( T, X ), Z ) ) ) ],
% 1.18/1.59 [ =( hAPP( 'c_Finite__Set_Ofold1'( X, Y ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 Y ), Z ), T ) ), 'c_Finite__Set_Ofold'( X, Z, T, Y, Y ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( Y ), Z ), T ) ), ~( 'c_Finite__Set_Ofinite'( T, Y ) ), ~(
% 1.18/1.59 'c_OrderedGroup_Oab__semigroup__mult'( X, Y ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( Z ), T ), 'c_HOL_Ominus__class_Ominus'( U, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( Z ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.18/1.59 'tc_bool' ) ) ), 'tc_fun'( Z, 'tc_bool' ) ) ), Z, Z ), W ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( Z ), T ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), U
% 1.18/1.59 ) ) ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, T, U, Z, Z ), W
% 1.18/1.59 ) ) ), ~( 'c_OrderedGroup_Oab__semigroup__mult'( X, Z ) ) ],
% 1.18/1.59 [ =( 'c_Map_Odom'( 'c_Fun_Ofun__upd'( X, Y, 'c_Option_Ooption_ONone'( Z
% 1.18/1.59 ), T, 'tc_Option_Ooption'( Z ) ), T, Z ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.59 'c_Map_Odom'( X, T, Z ), hAPP( hAPP( 'c_Set_Oinsert'( T ), Y ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ), 'tc_fun'( T
% 1.18/1.59 , 'tc_bool' ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold1'( 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.59 X ), Y ), hAPP( 'c_Finite__Set_Ofold1'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.59 X ), Z ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Z, X ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X ), hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), X ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Y ), Z ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), =( Z,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ =( 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.18/1.59 'tc_bool' ) ) ), 'tc_fun'( Y, 'tc_bool' ) ), Y ), 'c_Finite__Set_Ocard'(
% 1.18/1.59 X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), X ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( X, Y ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.59 'c_Finite__Set_Osetsum'( Y, 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( T ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.18/1.59 'tc_bool' ) ) ), 'tc_fun'( T, 'tc_bool' ) ), T, X ),
% 1.18/1.59 'c_Finite__Set_Osetsum'( Y, Z, T, X ) ), hBOOL( hAPP( hAPP( 'c_in'( T ),
% 1.18/1.59 U ), Z ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ) ],
% 1.18/1.59 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.59 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.59 't_a' ), 'tc_bool' ) ) ), 't_a' ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'(
% 1.18/1.59 X, hAPP( hAPP( 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) )
% 1.18/1.59 , 'c_Hoare__Mirabelle_Otriple_Otriple'( 'c_COMBK'( hAPP( 'c_COMBC'(
% 1.18/1.59 'c_fequal'( 'tc_Com_Ostate' ), 'tc_Com_Ostate', 'tc_Com_Ostate',
% 1.18/1.59 'tc_bool' ), 'v_sko__Hoare__Mirabelle__Xescape__2'( X, Y, T, Z ) ),
% 1.18/1.59 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 't_a' ), Z, 'c_COMBK'( hAPP( T,
% 1.18/1.59 'v_sko__Hoare__Mirabelle__Xescape__1'( X, Y, T, Z ) ), 'tc_fun'(
% 1.18/1.59 'tc_Com_Ostate', 'tc_bool' ), 't_a' ), 't_a' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.59 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ],
% 1.18/1.59 [ =( 'c_Map_Omap__add'( 'c_Fun_Ofun__upd'( X, Y, hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( Z ), T ), U, 'tc_Option_Ooption'( Z ) ), W, U,
% 1.18/1.59 Z ), 'c_Fun_Ofun__upd'( 'c_Map_Omap__add'( X, W, U, Z ), Y, hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( Z ), T ), U, 'tc_Option_Ooption'( Z ) ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_in'( U ), Y ), 'c_Map_Odom'( W, U, Z ) ) ) ],
% 1.18/1.59 [ =( 'c_Hoare__Mirabelle_OMGT'( 'v_c' ),
% 1.18/1.59 'c_Hoare__Mirabelle_Otriple_Otriple'( 'c_fequal'( 'tc_Com_Ostate' ),
% 1.18/1.59 'v_c', 'c_Natural_Oevalc'( 'v_c' ), 'tc_Com_Ostate' ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMax'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ) ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), hAPP(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMax'( X ), Y ) ), hAPP(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMax'( X ), Z ) ) ), =( Z,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMin'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ) ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), hAPP(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMin'( X ), Y ) ), hAPP(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMin'( X ), Z ) ) ), =( Z,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMin'( X ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 X ), Y ), Z ) ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y ),
% 1.18/1.59 hAPP( 'c_Finite__Set_Olinorder__class_OMin'( X ), Z ) ) ), =( Z,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMax'( X ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 X ), Y ), Z ) ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y ),
% 1.18/1.59 hAPP( 'c_Finite__Set_Olinorder__class_OMax'( X ), Z ) ) ), =( Z,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.59 [ =( 'c_Finite__Set_Ofold__image'( X, Y, Z, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 T ), U ), W ), V0, T ), hAPP( hAPP( X, hAPP( Y, U ) ),
% 1.18/1.59 'c_Finite__Set_Ofold__image'( X, Y, Z, W, V0, T ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( T ), U ), W ) ), ~( 'c_Finite__Set_Ofinite'( W, T ) ), ~(
% 1.18/1.59 'c_OrderedGroup_Oab__semigroup__mult'( X, V0 ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.59 , hAPP( 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X ), Y
% 1.18/1.59 ) ), hAPP( 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X
% 1.18/1.59 ), Z ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.59 ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ =( hAPP( 'c_Finite__Set_Ofold1'( X, Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ) ), hAPP( hAPP( X, hAPP( 'c_Finite__Set_Ofold1'( X, Y ), Z ) )
% 1.18/1.59 , hAPP( 'c_Finite__Set_Ofold1'( X, Y ), T ) ) ), =( T,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( T, Y ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ), ~(
% 1.18/1.59 'c_OrderedGroup_Oab__semigroup__idem__mult'( X, Y ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X ), hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.59 'c_HOL_Otimes__class_Otimes'( X ), X ), Z ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Z, X ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ =( hAPP( 'c_Finite__Set_Ofold1'( X, Y ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 Y ), Z ), T ) ), hAPP( hAPP( X, Z ), hAPP( 'c_Finite__Set_Ofold1'( X, Y )
% 1.18/1.59 , T ) ) ), ~( 'c_Finite__Set_Ofinite'( T, Y ) ), =( T,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_OrderedGroup_Oab__semigroup__idem__mult'( X, Y ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Z
% 1.18/1.59 ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.59 W, T ), U ) ) ) ), =( U, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.18/1.59 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ), ~(
% 1.18/1.59 'c_Lattices_Olower__semilattice'( X, V0, W, T ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y, Z, T, U ), hAPP( hAPP(
% 1.18/1.59 X, W ), V0 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), W ), Z ) ) ), ~(
% 1.18/1.59 hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y,
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_Set_Oinsert'( T ), W ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ), 'tc_fun'( T
% 1.18/1.59 , 'tc_bool' ) ), T, U ), V0 ) ) ) ],
% 1.18/1.59 [ =( 'c_Finite__Set_Osetsum'( X, 'c_HOL_Ominus__class_Ominus'( Y, hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( Z ), T ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.18/1.59 Z, 'tc_bool' ) ) ), 'tc_fun'( Z, 'tc_bool' ) ), Z, 'tc_nat' ),
% 1.18/1.59 'c_Finite__Set_Osetsum'( X, Y, Z, 'tc_nat' ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.18/1.59 Z ), T ), Y ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.59 ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.18/1.59 , 'tc_bool' ) ) ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.59 ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.18/1.59 , 'tc_bool' ) ) ), T ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), T ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' )
% 1.18/1.59 ), 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z
% 1.18/1.59 ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z
% 1.18/1.59 ), Y ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), Y ), hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_bool' ) ) ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_bool' ) ) ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.18/1.59 , 'tc_bool' ) ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ) ) ],
% 1.18/1.59 [ 'c_Nitpick_Ofold__graph_H'( X, Y, Z, hAPP( hAPP( X, T ), U ), W, V0 )
% 1.18/1.59 , ~( 'c_Nitpick_Ofold__graph_H'( X, Y, 'c_HOL_Ominus__class_Ominus'( Z,
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( W ), T ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( W, 'tc_bool' ) ) ), 'tc_fun'( W, 'tc_bool' ) ), U, W, V0 ) ),
% 1.18/1.59 ~( hBOOL( hAPP( hAPP( 'c_in'( W ), T ), Z ) ) ) ],
% 1.18/1.59 [ 'c_Map_Omap__le'( 'c_Fun_Ofun__upd'( X, Y, 'c_Option_Ooption_ONone'( Z
% 1.18/1.59 ), T, 'tc_Option_Ooption'( Z ) ), 'c_Fun_Ofun__upd'( U, Y, hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( Z ), W ), T, 'tc_Option_Ooption'( Z ) ), T, Z )
% 1.18/1.59 , ~( 'c_Map_Omap__le'( X, U, T, Z ) ) ],
% 1.18/1.59 [ 'c_Map_Omap__le'( X, Y, Z, T ), hBOOL( hAPP( hAPP( 'c_in'( Z ),
% 1.18/1.59 'c_Map_Osko__Map__Xmap__le__def__1__1'( X, Y, Z, T ) ), 'c_Map_Odom'( X,
% 1.18/1.59 Z, T ) ) ) ],
% 1.18/1.59 [ ~( =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), 'c_Map_Odom'( Y, X, Z ) ), 'c_Map_Odom'( T, X
% 1.18/1.59 , Z ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ),
% 1.18/1.59 =( 'c_Map_Omap__add'( Y, T, X, Z ), 'c_Map_Omap__add'( T, Y, X, Z ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( hAPP( 'c_Map_Omap__add'( X, Y, 't_a', Z ), 'v_x' ),
% 1.18/1.59 'c_Option_Ooption_Ooption__case'( hAPP( X, 'v_x' ),
% 1.18/1.59 'c_Option_Ooption_OSome'( Z ), hAPP( Y, 'v_x' ), 'tc_Option_Ooption'( Z )
% 1.18/1.59 , Z ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( 'c_Finite__Set_Ofold1Set'( X, Y, Z ),
% 1.18/1.59 'c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1'(
% 1.18/1.59 Y, X, Z ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.18/1.59 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( Z ), T ), U ), Z, Z ), hAPP( hAPP( X, Y ), W ) ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ), ~( hBOOL( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold__graph'( X, T, U, Z, Z ), W ) ) ), ~(
% 1.18/1.59 'c_OrderedGroup_Oab__semigroup__mult'( X, Z ) ) ],
% 1.18/1.59 [ =( 'c_Map_Odom'( 'c_Fun_Ofun__upd'( X, Y, Z, T, 'tc_Option_Ooption'( U
% 1.18/1.59 ) ), T, U ), hAPP( hAPP( 'c_Set_Oinsert'( T ), Y ), 'c_Map_Odom'( X, T,
% 1.18/1.59 U ) ) ), =( Z, 'c_Option_Ooption_ONone'( U ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( 'c_Finite__Set_Ofold1Set'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 Y ), Z ), T ), Y ), U ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), T ) ),
% 1.18/1.59 ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Z, T, Y, Y ), U ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( =( 'c_Map_Odom'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( Y, 'tc_bool' ) ) ) ), =( X, 'c_COMBK'( 'c_Option_Ooption_ONone'(
% 1.18/1.59 Z ), 'tc_Option_Ooption'( Z ), Y ) ) ],
% 1.18/1.59 [ =( 'c_Map_Odom'( 'c_COMBK'( 'c_Option_Ooption_ONone'( X ),
% 1.18/1.59 'tc_Option_Ooption'( X ), Y ), Y, X ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), Y ), hAPP( 'c_Finite__Set_Olinorder__class_OMax'( X
% 1.18/1.59 ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( X ), hAPP( 'c_Finite__Set_Olinorder__class_OMin'( X ), Y
% 1.18/1.59 ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMin'( X ), Y ), Z ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( X ), Z ), Y ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.18/1.59 'c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1'( Y,
% 1.18/1.59 Z, X ) ), Y ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMax'( X ), Y ), Z ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( X ), Z ), Y ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.18/1.59 'c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1'( Y,
% 1.18/1.59 Z, X ) ), Y ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ),
% 1.18/1.59 'c_Map_Osko__Map__XdomD__1__1'( Y, X, T, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( T ), Y ), 'c_Map_Odom'( X, T, Z ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( 'c_Finite__Set_Ofold1'( Y, X ),
% 1.18/1.59 Z ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( hAPP( Y,
% 1.18/1.59 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1'(
% 1.18/1.59 Y, X ) ),
% 1.18/1.59 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2'(
% 1.18/1.59 Y, X ) ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ),
% 1.18/1.59 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1'(
% 1.18/1.59 Y, X ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ),
% 1.18/1.59 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2'(
% 1.18/1.59 Y, X ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) )
% 1.18/1.59 ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), ~(
% 1.18/1.59 'c_OrderedGroup_Oab__semigroup__mult'( Y, X ) ) ],
% 1.18/1.59 [ =( hAPP( 'c_Map_Orestrict__map'( X, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( 't_a', 'tc_bool' ) ), 't_a', Y ), 'v_x' ),
% 1.18/1.59 'c_Option_Ooption_ONone'( Y ) ) ],
% 1.18/1.59 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.18/1.59 'c_Complete__Lattice_OInf__class_OInf'( hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.59 , Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), X ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( 'c_Finite__Set_Olattice_OSup__fin'( X, Y, Z ), hAPP( T, Y ) ), =( Y
% 1.18/1.59 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, Z ) ), ~(
% 1.18/1.59 'c_Complete__Lattice_Ocomplete__lattice'( U, T, W, V0, V1, X, V2, V3, Z )
% 1.18/1.59 ) ],
% 1.18/1.59 [ =( 'c_Finite__Set_Olattice_OInf__fin'( X, Y, Z ), hAPP( T, Y ) ), =( Y
% 1.18/1.59 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, Z ) ), ~(
% 1.18/1.59 'c_Complete__Lattice_Ocomplete__lattice'( T, U, W, V0, X, V1, V2, V3, Z )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Olattice__class_OInf__fin'( X ), Y ),
% 1.18/1.59 'c_Complete__Lattice_OInf__class_OInf'( Y, X ) ), =( Y,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'c_Orderings_Olinorder'( X, Y, Z ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Ofold1'( T, U ), hAPP( hAPP( 'c_Set_Oinsert'( U ), W ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ) ) ), W ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( 'c_Option_Oset'( hAPP( 'c_Option_Ooption_OSome'( X ), Y ), X ),
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.18/1.59 [ =( 'c_Set_Ovimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( Y ), X ), T ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, hAPP( 'c_Finite__Set_Ofold1'( Y, Z ), T ) ), U )
% 1.18/1.59 ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), T ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( T, Z ) ), ~( 'c_Lattices_Olower__semilattice'( X
% 1.18/1.59 , W, Y, Z ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ), 'c_SetInterval_Oord__class_OlessThan'( Y, X
% 1.18/1.59 ), 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.18/1.59 , 'tc_bool' ) ) ), T ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.59 'tc_fun'( 't_a', 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a',
% 1.18/1.59 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool' ), X ) ), hAPP( 'c_COMBC'( 'c_in'(
% 1.18/1.59 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool' ), Y ) ), 'v_x' )
% 1.18/1.59 , hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( 't_a', 'tc_bool'
% 1.18/1.59 ) ), X ), Y ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), Z ), 'c_Finite__Set_Ofold'( 'c_Set_Oinsert'( X ),
% 1.18/1.59 Z, Y, X, 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.18/1.59 'c_Complete__Lattice_OSup__class_OSup'( hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.59 , Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), X ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.18/1.59 'c_Finite__Set_Ofold'( 'c_Lattices_Oupper__semilattice__class_Osup'( X )
% 1.18/1.59 , Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ), X, X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ),
% 1.18/1.59 'c_Finite__Set_Ofold'( 'c_Lattices_Oupper__semilattice__class_Osup'( X )
% 1.18/1.59 , Y, T, X, X ) ) ), ~( 'c_Finite__Set_Ofinite'( T, X ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP(
% 1.18/1.59 'c_Finite__Set_Olattice__class_OInf__fin'( X ), Z ) ), Y ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, X )
% 1.18/1.59 ) ],
% 1.18/1.59 [ =( 'c_Finite__Set_Ocard'( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ),
% 1.18/1.59 X ), 'c_Finite__Set_Ocard'( Z, X ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.18/1.59 Y ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.18/1.59 [ =( 'c_Map_Odom'( 'c_Fun_Ofun__upd'( 'c_COMBK'(
% 1.18/1.59 'c_Option_Ooption_ONone'( X ), 'tc_Option_Ooption'( X ), Y ), Z, hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( X ), T ), Y, 'tc_Option_Ooption'( X ) ), Y, X )
% 1.18/1.59 , hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( Y, 'tc_bool' ) ) ) ) ],
% 1.18/1.59 [ =( 'c_Fun_Ofun__upd'( 'c_Map_Orestrict__map'( X, Y, Z, T ), U,
% 1.18/1.59 'c_Option_Ooption_ONone'( T ), Z, 'tc_Option_Ooption'( T ) ),
% 1.18/1.59 'c_Map_Orestrict__map'( X, 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( Z ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.18/1.59 'tc_bool' ) ) ), 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( Z ), U ), Y ) ) ) ],
% 1.18/1.59 [ =( 'c_Suc'( 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( Y, 'tc_bool' ) ) ), 'tc_fun'( Y, 'tc_bool' ) ), Y ) ),
% 1.18/1.59 'c_Finite__Set_Ocard'( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ),
% 1.18/1.59 X ) ) ), ~( 'c_Finite__Set_Ofinite'( X, Y ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.18/1.59 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.18/1.59 'tc_bool' ) ) ), 'tc_fun'( Y, 'tc_bool' ) ), Y ) ), 'c_Finite__Set_Ocard'(
% 1.18/1.59 X, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), X ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( X, Y ) ) ],
% 1.18/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 'c_Finite__Set_Osetprod'(
% 1.18/1.59 Y, 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_Set_Oinsert'( T ), U )
% 1.18/1.59 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ), 'tc_fun'(
% 1.18/1.59 T, 'tc_bool' ) ), T, X ), 'c_Finite__Set_Osetprod'( Y, Z, T, X ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_in'( T ), U ), Z ) ), =( hAPP( Y, U ),
% 1.18/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( 'c_Finite__Set_Ofold'( X, Y, Z, T, U ), hAPP( hAPP( X, W ),
% 1.18/1.59 'c_Finite__Set_Ofold'( X, Y, 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( T ), W ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.18/1.59 'tc_bool' ) ) ), 'tc_fun'( T, 'tc_bool' ) ), T, U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( T ), W ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ),
% 1.18/1.59 ~( 'c_Finite__Set_Ofun__left__comm'( X, T, U ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.18/1.59 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), 'tc_fun'( Y
% 1.18/1.59 , 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'( Y ), T ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), 'tc_fun'( Y
% 1.18/1.59 , 'tc_bool' ) ), Y ) ), 'c_Finite__Set_Ocard'( X, Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( Y ), T ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ),
% 1.18/1.59 X ) ) ), ~( 'c_Finite__Set_Ofinite'( X, Y ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.59 'c_Finite__Set_Osetsum'( Y, Z, T, X ), hAPP( hAPP(
% 1.18/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, U ) ), 'c_Finite__Set_Osetsum'(
% 1.18/1.59 Y, 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_Set_Oinsert'( T ), U )
% 1.18/1.59 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ), 'tc_fun'(
% 1.18/1.59 T, 'tc_bool' ) ), T, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), U ), Z )
% 1.18/1.59 ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_fun'( Y, 'tc_bool' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.59 ) ) ), Y ), Y ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ), Y ) ],
% 1.18/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ ~( hBOOL( hAPP( 'c_Finite__Set_Ofold1Set'( X,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ), Z ) ) )
% 1.18/1.59 ],
% 1.18/1.59 [ =( hAPP( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.59 ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( T, X, U, W, V0, V1
% 1.18/1.59 , Z, V2, Y ) ) ],
% 1.18/1.59 [ =( hAPP( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.59 ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X, T, U, W, V0, V1
% 1.18/1.59 , V2, Z, Y ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.59 ) ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.18/1.59 'tc_bool' ) ), Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.18/1.59 'tc_bool' ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( X ) ), Y ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( X ) ), Y ), Y ) ],
% 1.18/1.59 [ =( hAPP( 'c_Finite__Set_Ofold1'( X, Y ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 Y ), Z ), T ) ), hAPP( hAPP( X, Z ), hAPP( 'c_Finite__Set_Ofold1'( X, Y )
% 1.18/1.59 , T ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), T ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( T, Y ) ), =( T, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_OrderedGroup_Oab__semigroup__mult'( X
% 1.18/1.59 , Y ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP( 'c_in'( X )
% 1.18/1.59 , hAPP( 'c_Finite__Set_Olinorder__class_OMax'( X ), Y ) ), Y ) ), =( Y,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP( 'c_in'( X )
% 1.18/1.59 , hAPP( 'c_Finite__Set_Olinorder__class_OMin'( X ), Y ) ), Y ) ), =( Y,
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( U ), Y ), T ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W
% 1.18/1.59 , Z, X, V0, V1, V2, V3, V4, U ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( U ), T ), Z ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( Y
% 1.18/1.59 , W, X, V0, V1, V2, V3, V4, U ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.18/1.59 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.18/1.59 T, 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T
% 1.18/1.59 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.18/1.59 T, 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T
% 1.18/1.59 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ) ) ) ],
% 1.18/1.59 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( T, Z, 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.18/1.59 X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , T ), Z ) ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.18/1.59 [ 'c_Map_Omap__le'( 'c_Map_Omap__add'( X, Y, Z, T ), U, Z, T ), ~(
% 1.18/1.59 'c_Map_Omap__le'( X, 'c_Map_Omap__add'( X, Y, Z, T ), Z, T ) ), ~(
% 1.18/1.59 'c_Map_Omap__le'( Y, U, Z, T ) ), ~( 'c_Map_Omap__le'( X, U, Z, T ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'c_Map_Omap__le'( X, 'c_Map_Omap__add'( Y, X, Z, T ), Z, T ) ],
% 1.18/1.59 [ ~( =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ), T ) ) ), =(
% 1.18/1.59 hAPP( 'c_Map_Omap__add'( U, X, W, Z ), Y ), hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( Z ), T ) ) ],
% 1.18/1.59 [ ~( =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ), T ) ) ), =(
% 1.18/1.59 hAPP( 'c_Map_Omap__add'( U, X, W, Z ), Y ), hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( Z ), T ) ) ],
% 1.18/1.59 [ ~( =( hAPP( X, Y ), 'c_Option_Ooption_ONone'( Z ) ) ), ~( =( hAPP( T,
% 1.18/1.59 Y ), 'c_Option_Ooption_ONone'( Z ) ) ), =( hAPP( 'c_Map_Omap__add'( X, T
% 1.18/1.59 , U, Z ), Y ), 'c_Option_Ooption_ONone'( Z ) ) ],
% 1.18/1.59 [ =( 'c_Set_Ovimage'( X, hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ), U, Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.18/1.59 , 'c_Set_Ovimage'( X, Z, U, Y ) ), 'c_Set_Ovimage'( X, T, U, Y ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ), 'c_Finite__Set_Ofinite'(
% 1.18/1.59 Y, X ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Z ), Y ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.18/1.59 [ ~( 'class_HOL_Ominus'( X ) ), =( hAPP( 'c_HOL_Ominus__class_Ominus'( Y
% 1.18/1.59 , Z, 'tc_fun'( 't_a', X ) ), 'v_x' ), 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.18/1.59 Y, 'v_x' ), hAPP( Z, 'v_x' ), X ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ) ) ],
% 1.18/1.59 [ ~( =( hAPP( 'c_Map_Omap__add'( X, Y, Z, T ), U ),
% 1.18/1.59 'c_Option_Ooption_ONone'( T ) ) ), =( hAPP( Y, U ),
% 1.18/1.59 'c_Option_Ooption_ONone'( T ) ) ],
% 1.18/1.59 [ ~( =( hAPP( 'c_Map_Omap__add'( X, Y, Z, T ), U ),
% 1.18/1.59 'c_Option_Ooption_ONone'( T ) ) ), =( hAPP( X, U ),
% 1.18/1.59 'c_Option_Ooption_ONone'( T ) ) ],
% 1.18/1.59 [ ~( =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ), T ) ) ), ~(
% 1.18/1.59 =( hAPP( U, Y ), 'c_Option_Ooption_ONone'( Z ) ) ), =( hAPP(
% 1.18/1.59 'c_Map_Omap__add'( X, U, W, Z ), Y ), hAPP( 'c_Option_Ooption_OSome'( Z )
% 1.18/1.59 , T ) ) ],
% 1.18/1.59 [ ~( =( hAPP( 'c_Map_Omap__add'( X, Y, Z, T ), U ), hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( T ), W ) ) ), =( hAPP( X, U ), hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( T ), W ) ), =( hAPP( Y, U ), hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( T ), W ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Z ), T ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Z ), T ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), T ) ) ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.18/1.59 , T, X ) ) ), =( Z, T ) ],
% 1.18/1.59 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.18/1.59 , T, X ) ) ), =( Y, Z ) ],
% 1.18/1.59 [ ~( =( 'c_Option_Ooption_ONone'( X ), hAPP( 'c_Option_Ooption_OSome'( X
% 1.18/1.59 ), Y ) ) ) ],
% 1.18/1.59 [ ~( =( 'c_Option_Ooption_ONone'( X ), hAPP( 'c_Option_Ooption_OSome'( X
% 1.18/1.59 ), Y ) ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.18/1.59 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Y ), Y ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.59 X, 'tc_bool' ) ), Y ), Y ), Y ) ],
% 1.18/1.59 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( 't_a', X ) ), Y )
% 1.18/1.59 , Z ), 'v_x' ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.59 X ), hAPP( Y, 'v_x' ) ), hAPP( Z, 'v_x' ) ) ) ],
% 1.18/1.59 [ =( hAPP( 'c_Finite__Set_Ofold1'( X, Y ), Z ), 'c_The'(
% 1.18/1.59 'c_Finite__Set_Ofold1Set'( X, Z, Y ), Y ) ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 1.18/1.59 Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ) ],
% 1.18/1.59 [ =( 'c_Set_Ovimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T
% 1.18/1.59 , 'tc_bool' ) ), U, T ), 'c_HOL_Ominus__class_Ominus'( 'c_Set_Ovimage'( X
% 1.18/1.59 , Y, U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U, 'tc_bool' ) ) )
% 1.18/1.59 ],
% 1.18/1.59 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ), =( Y
% 1.18/1.59 , T ) ],
% 1.18/1.59 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ), =( X
% 1.18/1.59 , Z ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ), Y ) ),
% 1.18/1.59 ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 1.18/1.59 Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.18/1.59 [ 'c_Map_Omap__le'( X, Y, Z, T ), ~( 'c_Map_Omap__le'( 'c_Map_Omap__add'(
% 1.18/1.59 U, X, Z, T ), Y, Z, T ) ) ],
% 1.18/1.59 [ 'c_Map_Omap__le'( X, X, Y, Z ) ],
% 1.18/1.59 [ 'c_Map_Omap__le'( X, Y, Z, T ), ~( 'c_Map_Omap__le'( U, Y, Z, T ) ),
% 1.18/1.59 ~( 'c_Map_Omap__le'( X, U, Z, T ) ) ],
% 1.18/1.59 [ =( 'c_Map_Odom'( 'c_Map_Omap__add'( X, Y, Z, T ), Z, T ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.18/1.59 , 'c_Map_Odom'( Y, Z, T ) ), 'c_Map_Odom'( X, Z, T ) ) ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.18/1.59 [ ~( =( hAPP( 'c_Option_Ooption_OSome'( X ), Y ),
% 1.18/1.59 'c_Option_Ooption_ONone'( X ) ) ) ],
% 1.18/1.59 [ ~( =( hAPP( 'c_Option_Ooption_OSome'( X ), Y ),
% 1.18/1.59 'c_Option_Ooption_ONone'( X ) ) ) ],
% 1.18/1.59 [ ~( =( hAPP( 'c_Option_Ooption_OSome'( X ), Y ), hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( X ), Z ) ) ), =( Y, Z ) ],
% 1.18/1.59 [ =( 'c_Map_Omap__add'( X, 'c_Map_Omap__add'( Y, Z, T, U ), T, U ),
% 1.18/1.59 'c_Map_Omap__add'( 'c_Map_Omap__add'( X, Y, T, U ), Z, T, U ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.18/1.59 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_OrderedGroup_Oab__semigroup__mult'( X
% 1.18/1.59 , U ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.18/1.59 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_OrderedGroup_Oab__semigroup__mult'( X
% 1.18/1.59 , U ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.18/1.59 'c_OrderedGroup_Oab__semigroup__mult'( X, T ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( T,
% 1.18/1.59 'tc_bool' ) ), Z ), X ), Y ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), T ) ), ~( hBOOL( hAPP( Z, T ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ hBOOL( hAPP( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'( hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y,
% 1.18/1.59 'tc_bool' ) ), X ), Z ), Y ) ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'( hAPP(
% 1.18/1.59 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y,
% 1.18/1.59 'tc_bool' ) ), Z ), X ), Y ) ) ],
% 1.18/1.59 [ =( 'c_Map_Omap__add'( X, Y, Z, T ), 'c_Map_Omap__add'( Y, X, Z, T ) )
% 1.18/1.59 , ~( 'c_Map_Omap__le'( X, 'c_Map_Omap__add'( X, Y, Z, T ), Z, T ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ ~( =( 'c_Map_Omap__add'( X, Y, Z, T ), 'c_Map_Omap__add'( Y, X, Z, T )
% 1.18/1.59 ) ), 'c_Map_Omap__le'( X, 'c_Map_Omap__add'( X, Y, Z, T ), Z, T ) ],
% 1.18/1.59 [ =( X, Y ), ~( 'c_Map_Omap__le'( Y, X, Z, T ) ), ~( 'c_Map_Omap__le'( X
% 1.18/1.59 , Y, Z, T ) ) ],
% 1.18/1.59 [ ~( =( hAPP( 'c_Map_Omap__add'( X, Y, Z, T ), U ), hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( T ), W ) ) ), =( hAPP( Y, U ),
% 1.18/1.59 'c_Option_Ooption_ONone'( T ) ), =( hAPP( Y, U ), hAPP(
% 1.18/1.59 'c_Option_Ooption_OSome'( T ), W ) ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 1.18/1.59 Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_Set_Oinsert'( Z ), T ), Y
% 1.18/1.59 ), 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 1.18/1.59 [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( Y ), Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), Y ), ~(
% 1.18/1.59 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Y
% 1.18/1.59 , 'tc_bool' ) ), Y ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( X, hAPP( Y, Z ) ) ), ~( hBOOL( hAPP( 'c_Set_Ovimage'( Y,
% 1.18/1.59 X, T, U ), Z ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( 'c_Set_Ovimage'( X, Y, Z, T ), U ) ), ~( hBOOL( hAPP( Y,
% 1.18/1.59 hAPP( X, U ) ) ) ) ],
% 1.18/1.59 [ =( 'c_The'( hAPP( 'c_fequal'( X ), Y ), X ), Y ) ],
% 1.18/1.59 [ =( 'c_Option_Othe'( hAPP( 'c_Option_Ooption_OSome'( X ), Y ), X ), Y )
% 1.18/1.59 ],
% 1.18/1.59 [ hBOOL( hAPP( 'c_Finite__Set_Ofold1Set'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), Y
% 1.18/1.59 ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMin'( X ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 X ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) )
% 1.18/1.59 , Y ) ],
% 1.18/1.59 [ =( 'c_The'( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), X ), Y ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( hAPP( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( Y ), T ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.18/1.59 'tc_bool' ) ) ) ) ), hAPP( hAPP( U, Z ), T ) ), ~(
% 1.18/1.59 'c_Complete__Lattice_Ocomplete__lattice'( X, W, V0, V1, U, V2, V3, V4, Y
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ =( hAPP( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( Y ), T ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.18/1.59 'tc_bool' ) ) ) ) ), hAPP( hAPP( U, Z ), T ) ), ~(
% 1.18/1.59 'c_Complete__Lattice_Ocomplete__lattice'( W, X, V0, V1, V2, U, V3, V4, Y
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ),
% 1.18/1.59 Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), 'tc_fun'( Y
% 1.18/1.59 , 'tc_bool' ) ), T, 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ),
% 1.18/1.59 Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.59 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Y, 'tc_bool' ) ), hAPP(
% 1.18/1.59 hAPP( 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.18/1.59 Y, 'tc_bool' ) ) ), 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.18/1.59 [ =( X, Y ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold1Set'( Z, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( T ), X ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.18/1.59 'tc_bool' ) ) ), T ), Y ) ) ) ],
% 1.18/1.59 [ =( 'c_Set_Ocontents'( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), X ), Y ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( X, 'c_Nitpick_Osko__Nitpick__XEx1__def__1__3'( hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.18/1.59 'tc_bool' ) ) ), Y ) ), ~( hBOOL( hAPP( hAPP( hAPP( 'c_Set_Oinsert'( Y )
% 1.18/1.59 , Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), X )
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ =( hAPP( 'c_Finite__Set_Ofold1'( X, Y ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) )
% 1.18/1.59 , Z ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.18/1.59 'c_Finite__Set_Olinorder__class_OMax'( X ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 X ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) )
% 1.18/1.59 , Y ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.59 Z, hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_bool' ) ) ), hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( X ), Y ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.18/1.59 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Y, X ), hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.59 'tc_bool' ) ) ) ) ],
% 1.18/1.59 [ =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.59 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.59 , hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.59 'tc_fun'( X, 'tc_bool' ) ) ) ), Z ) ) ],
% 1.18/1.59 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.18/1.59 'c_Complete__Lattice_OInf__class_OInf'( hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.59 , Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), X )
% 1.18/1.59 , Y ) ],
% 1.18/1.59 [ =( hAPP( 'c_Map_Omap__add'( X, Y, Z, T ), U ), hAPP( X, U ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_in'( Z ), U ), 'c_Map_Odom'( Y, Z, T ) ) ) ],
% 1.18/1.59 [ =( hAPP( 'c_Map_Omap__add'( X, Y, Z, T ), U ), hAPP( Y, U ) ), hBOOL(
% 1.18/1.59 hAPP( hAPP( 'c_in'( Z ), U ), 'c_Map_Odom'( X, Z, T ) ) ) ],
% 1.18/1.59 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Map_Odom'( Z, X, T ) ) ), =(
% 1.18/1.59 hAPP( Z, Y ), 'c_Option_Ooption_ONone'( T ) ) ],
% 1.18/1.59 [ ~( =( hAPP( X, Y ), 'c_Option_Ooption_ONone'( Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.59 hAPP( 'c_in'( T ), Y ), 'c_Map_Odom'( X, T, Z ) ) ) ) ],
% 1.18/1.59 [ ~( =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ), T ) ) ),
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_in'( U ), Y ), 'c_Map_Odom'( X, U, Z ) ) ) ],
% 1.18/1.59 [ =( hAPP( X, Y ), hAPP( Z, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y
% 1.18/1.59 ), 'c_Map_Odom'( X, T, U ) ) ) ), ~( 'c_Map_Omap__le'( X, Z, T, U ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ =( hAPP( 'c_Map_Omap__add'( X, Y, Z, T ), U ), hAPP( Y, U ) ), ~(
% 1.18/1.59 hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), 'c_Map_Odom'( Y, Z, T ) ) ) ) ],
% 1.18/1.59 [ ~( =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ), T ) ) ), =(
% 1.18/1.59 hAPP( hAPP( 'c_Set_Oinsert'( U ), Y ), 'c_Map_Odom'( X, U, Z ) ),
% 1.18/1.59 'c_Map_Odom'( X, U, Z ) ) ],
% 1.18/1.59 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.59 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.59 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( U, W ),
% 1.18/1.59 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3'( X, Y, T, Z, V0, U
% 1.18/1.59 ) ) ), ~( hBOOL( hAPP( hAPP( V0, W ),
% 1.18/1.59 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2'( X, Y, T, Z ) ) ) )
% 1.18/1.59 , ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.59 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, Z, U, 't_a' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.59 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ],
% 1.18/1.59 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.59 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.59 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( U, W ),
% 1.18/1.59 'v_sko__Hoare__Mirabelle__Xconseq12__3'( Y, V0, T, U ) ) ), ~( hBOOL(
% 1.18/1.59 hAPP( hAPP( V0, W ), 'v_sko__Hoare__Mirabelle__Xconseq12__2'( Y, V0, T, U
% 1.18/1.59 ) ) ) ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.59 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, Z, U, 't_a' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.59 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ],
% 1.18/1.59 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.59 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.59 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( U, W ),
% 1.18/1.59 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3'( X, Y, T, Z, V0
% 1.18/1.59 , U ) ) ), ~( hBOOL( hAPP( hAPP( V0, W ),
% 1.18/1.59 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2'( X, Y, T, Z ) )
% 1.18/1.59 ) ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.59 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, Z, U, 't_a' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.59 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ],
% 1.18/1.59 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.59 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.59 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( Y,
% 1.18/1.59 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1'( X, Y, T, Z ) )
% 1.18/1.59 , 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2'( X, Y, T, Z )
% 1.18/1.59 ) ) ],
% 1.18/1.59 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.59 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.59 't_a' ), 'tc_bool' ) ) ), 't_a' ), ~( hBOOL( hAPP( hAPP( T,
% 1.18/1.59 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1'( X, Y, T, Z ) )
% 1.18/1.59 , 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3'( X, Y, T, Z, U
% 1.18/1.59 , W ) ) ) ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.18/1.59 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.59 'c_Hoare__Mirabelle_Otriple_Otriple'( U, Z, W, 't_a' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.59 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ],
% 1.18/1.59 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.59 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.59 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( Y,
% 1.18/1.59 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1'( X, Y, T, Z ) ),
% 1.18/1.59 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2'( X, Y, T, Z ) ) ) ]
% 1.18/1.59 ,
% 1.18/1.59 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.59 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.59 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.59 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.59 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( U,
% 1.18/1.59 'v_sko__Hoare__Mirabelle__Xconseq2__1'( T, U ) ),
% 1.18/1.59 'v_sko__Hoare__Mirabelle__Xconseq2__2'( T, U ) ) ), ~(
% 1.18/1.59 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, U, 't_a' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( Y,
% 1.18/1.60 'v_sko__Hoare__Mirabelle__Xconseq12__1'( Y, U, T, W ) ),
% 1.18/1.60 'v_sko__Hoare__Mirabelle__Xconseq12__2'( Y, U, T, W ) ) ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( U, Z, W, 't_a' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( Y,
% 1.18/1.60 'v_sko__Hoare__Mirabelle__Xconseq1__1'( Y, U ) ),
% 1.18/1.60 'v_sko__Hoare__Mirabelle__Xconseq1__2'( Y, U ) ) ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( U, Z, T, 't_a' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 't_a' ), 'tc_bool' ) ) ), 't_a' ), ~( hBOOL( hAPP( hAPP( T,
% 1.18/1.60 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1'( X, Y, T, Z ) ),
% 1.18/1.60 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3'( X, Y, T, Z, U, W )
% 1.18/1.60 ) ) ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( U, Z, W, 't_a' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 't_a' ), 'tc_bool' ) ) ), 't_a' ), ~( hBOOL( hAPP( hAPP( U,
% 1.18/1.60 'v_sko__Hoare__Mirabelle__Xconseq1__1'( Y, U ) ),
% 1.18/1.60 'v_sko__Hoare__Mirabelle__Xconseq1__2'( Y, U ) ) ) ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( U, Z, T, 't_a' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 't_a' ), 'tc_bool' ) ) ), 't_a' ), ~( hBOOL( hAPP( hAPP( T,
% 1.18/1.60 'v_sko__Hoare__Mirabelle__Xconseq12__1'( Y, U, T, W ) ),
% 1.18/1.60 'v_sko__Hoare__Mirabelle__Xconseq12__3'( Y, U, T, W ) ) ) ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( U, Z, W, 't_a' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 't_a' ), 'tc_bool' ) ) ), 't_a' ), ~( hBOOL( hAPP( hAPP( T,
% 1.18/1.60 'v_sko__Hoare__Mirabelle__Xconseq2__1'( T, U ) ),
% 1.18/1.60 'v_sko__Hoare__Mirabelle__Xconseq2__2'( T, U ) ) ) ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, U, 't_a' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( Y,
% 1.18/1.60 'v_sko__Hoare__Mirabelle__Xescape__1'( X, Y, T, Z ) ),
% 1.18/1.60 'v_sko__Hoare__Mirabelle__Xescape__2'( X, Y, T, Z ) ) ) ],
% 1.18/1.60 [ =( 'c_Hoare__Mirabelle_OMGT'( X ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( 'c_fequal'( 'tc_Com_Ostate' ), X,
% 1.18/1.60 'c_Natural_Oevalc'( X ), 'tc_Com_Ostate' ) ) ],
% 1.18/1.60 [ =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.60 Z, hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.60 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_bool' ) ) ), Z ), ~( hBOOL(
% 1.18/1.60 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.18/1.60 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ),
% 1.18/1.60 'c_Set_Ovimage'( X, hAPP( hAPP( 'c_Set_Oinsert'( U ), Z ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ) ), T, U ) ) )
% 1.18/1.60 ) ],
% 1.18/1.60 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( T ), hAPP( Z, Y ) ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.60 'tc_fun'( T, 'tc_bool' ) ) ), X, T ) ) ) ],
% 1.18/1.60 [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL(
% 1.18/1.60 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~(
% 1.18/1.60 'c_OrderedGroup_Oab__semigroup__mult'( T, U ) ) ],
% 1.18/1.60 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y )
% 1.18/1.60 , Z ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.18/1.60 , 'tc_bool' ) ), Z ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( 'c_Orderings_Obot__class_Obot'(
% 1.18/1.60 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) )
% 1.18/1.60 , hAPP( hAPP( 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 'tc_Com_Ostate' ) ), 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z,
% 1.18/1.60 'tc_Com_Ostate' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) ) ),
% 1.18/1.60 'tc_Com_Ostate' ), ~( 'c_Hoare__Mirabelle_Ohoare__valids'(
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 'tc_Com_Ostate' ), 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, 'tc_Com_Ostate' ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 'tc_Com_Ostate' ), 'tc_bool' ) ) ), 'tc_Com_Ostate' ) ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( 'c_Orderings_Obot__class_Obot'(
% 1.18/1.60 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) )
% 1.18/1.60 , hAPP( hAPP( 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 'tc_Com_Ostate' ) ), 'c_Hoare__Mirabelle_OMGT'( Y ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 'tc_Com_Ostate' ), 'tc_bool' ) ) ), 'tc_Com_Ostate' ) ) ],
% 1.18/1.60 [ hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( 'c_Com_Ocom_OBODY'( X ) ), Y )
% 1.18/1.60 , Z ) ), ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( 'c_Option_Othe'( hAPP(
% 1.18/1.60 'c_Com_Obody', X ), 'tc_Com_Ocom' ) ), Y ), Z ) ) ) ],
% 1.18/1.60 [ hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( 'c_Option_Othe'( hAPP(
% 1.18/1.60 'c_Com_Obody', X ), 'tc_Com_Ocom' ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.60 'c_Natural_Oevalc'( 'c_Com_Ocom_OBODY'( X ) ), Y ), Z ) ) ) ],
% 1.18/1.60 [ 'c_Finite__Set_Ofinite'( 'c_Map_Odom'( 'c_Com_Obody', 'tc_Com_Opname'
% 1.18/1.60 , 'tc_Com_Ocom' ), 'tc_Com_Opname' ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, 'c_Com_Ocom_OSemi'( T, U ), W, Y
% 1.18/1.60 ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ) ), Y ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, U, W, Y ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 Y ), 'tc_bool' ) ) ), Y ) ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( X,
% 1.18/1.60 hAPP( hAPP( 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, T, V0, Y ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 Y ), 'tc_bool' ) ) ), Y ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, 'c_Com_Ocom_OBODY'( T ), U, Y )
% 1.18/1.60 ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ) ), Y ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, 'c_Com_Ocom_OBODY'( T ), U, Y )
% 1.18/1.60 ), X ), hAPP( hAPP( 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( Y )
% 1.18/1.60 ), 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, 'c_Option_Othe'( hAPP(
% 1.18/1.60 'c_Com_Obody', T ), 'tc_Com_Ocom' ), U, Y ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 Y ), 'tc_bool' ) ) ), Y ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, 'c_Com_Ocom_OBODY'( T ), U, Y )
% 1.18/1.60 ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ) ), Y ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, 'c_Option_Othe'( hAPP(
% 1.18/1.60 'c_Com_Obody', T ), 'tc_Com_Ocom' ), U, Y ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 Y ), 'tc_bool' ) ) ), Y ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Z ), T ), Y ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( X, T, Y ) ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.60 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ) ), Y ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Z ) ), T ), Y ), Z ) ) ],
% 1.18/1.60 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSKIP' ) ) ],
% 1.18/1.60 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.60 , Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.60 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.18/1.60 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.60 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.18/1.60 [ hBOOL( hAPP( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ), Y ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, 'c_Com_Ocom_OSKIP', Z, Y ) ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.18/1.60 Y ), 'tc_bool' ) ) ), Y ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( X, T, Z ) ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( T, Y, Z ) ) ],
% 1.18/1.60 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.60 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.18/1.60 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.18/1.60 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.60 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.18/1.60 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.60 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.18/1.60 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.18/1.60 hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ) ) ],
% 1.18/1.60 [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( Z, V0 ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( Y, W ) ],
% 1.18/1.60 [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( X, U ) ],
% 1.18/1.60 [ =( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' )
% 1.18/1.60 ), 'v_x' ), hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' ) ) ) ) ],
% 1.18/1.60 [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.60 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( X ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.60 'tc_bool' ) ) ) ) ) ), =( Z, T ), =( Z, U ) ],
% 1.18/1.60 [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.60 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( X ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.60 'tc_bool' ) ) ) ) ) ), =( Y, U ), =( Z, U ) ],
% 1.18/1.60 [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.60 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( X ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.60 'tc_bool' ) ) ) ) ) ), =( Z, T ), =( Y, T ) ],
% 1.18/1.60 [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.60 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( X ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.60 'tc_bool' ) ) ) ) ) ), =( Y, U ), =( Y, T ) ],
% 1.18/1.60 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( Z ), T ), X ) ) )
% 1.18/1.60 , ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( Z ), T ), Y ) ) ) ],
% 1.18/1.60 [ hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP' ), X ), X )
% 1.18/1.60 ) ],
% 1.18/1.60 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), =( Y, T ), ~( hBOOL( hAPP(
% 1.18/1.60 hAPP( 'c_in'( X ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), Z ) ) ) )
% 1.18/1.60 ],
% 1.18/1.60 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.60 ) ), Y ) ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.60 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ), Y ) ],
% 1.18/1.60 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( T ), Z ), X ), Y ) ) ) ],
% 1.18/1.60 [ =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 X ), Y ), Z ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ) ],
% 1.18/1.60 [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.18/1.60 [ ~( 'class_Orderings_Obot'( X ) ), =( hAPP(
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.18/1.60 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( Z ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.18/1.60 'tc_bool' ) ) ) ) ) ) ],
% 1.18/1.60 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.60 , Y ), Z ) ) ) ],
% 1.18/1.60 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.60 , Y ), Z ) ) ) ],
% 1.18/1.60 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.60 , Y ), Z ) ) ) ],
% 1.18/1.60 [ =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 X ), Z ), T ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( X ), Y ), T ) ) ) ],
% 1.18/1.60 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( Z, Y ) ) )
% 1.18/1.60 ],
% 1.18/1.60 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), X ) ) )
% 1.18/1.60 ],
% 1.18/1.60 [ =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) )
% 1.18/1.60 , hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.60 , Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.60 'tc_bool' ) ) ) ) ), =( Y, Z ) ],
% 1.18/1.60 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.18/1.60 [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ),
% 1.18/1.60 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL(
% 1.18/1.60 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.60 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ) ), Y ), ~(
% 1.18/1.60 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Z ), T ), Y ) ) ],
% 1.18/1.60 [ hBOOL( hAPP( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ), T ) ), ~(
% 1.18/1.60 hBOOL( hAPP( Z, T ) ) ) ],
% 1.18/1.60 [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( X ), Y ), T ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.18/1.60 T ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), =( Z, T ) ],
% 1.18/1.60 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OBODY'( Y ) ) ), =( X, Y )
% 1.18/1.60 ],
% 1.18/1.60 [ =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ), Z ), ~( hBOOL( hAPP(
% 1.18/1.60 hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.18/1.60 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OBODY'( X ) ) ) ],
% 1.18/1.60 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'(
% 1.18/1.60 'c_Com_Ocom_OSKIP' ), Y ), X ) ) ) ],
% 1.18/1.60 [ ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP' ), 'v_x'
% 1.18/1.60 ), 'v_x' ) ) ) ],
% 1.18/1.60 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( 'v_G', hAPP( hAPP(
% 1.18/1.60 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ),
% 1.18/1.60 'c_Hoare__Mirabelle_Otriple_Otriple'( 'c_fequal'( 'tc_Com_Ostate' ),
% 1.18/1.60 'c_Com_Ocom_OBODY'( X ), 'c_Natural_Oevalc'( 'c_Com_Ocom_OBODY'( X ) ),
% 1.18/1.60 'tc_Com_Ostate' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.18/1.60 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) ) ),
% 1.18/1.60 'tc_Com_Ostate' ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_Com_Opname' ), X ),
% 1.18/1.60 'c_Map_Odom'( 'c_Com_Obody', 'tc_Com_Opname', 'tc_Com_Ocom' ) ) ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.18/1.60 'class_Complete__Lattice_Ocomplete__lattice'( Y ) ) ],
% 1.18/1.60 [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.18/1.60 'class_Lattices_Olattice'( Y ) ) ],
% 1.18/1.60 [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.18/1.60 'class_Lattices_Olattice'( Y ) ) ],
% 1.18/1.60 [ 'class_Lattices_Odistrib__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.18/1.60 'class_Lattices_Odistrib__lattice'( Y ) ) ],
% 1.18/1.60 [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.18/1.60 'class_Lattices_Obounded__lattice'( Y ) ) ],
% 1.18/1.60 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_fun'( X, Y ) ), ~(
% 1.18/1.60 'class_Finite__Set_Ofinite_Ofinite'( Y ) ), ~(
% 1.18/1.60 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ],
% 1.18/1.60 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.18/1.60 'class_Orderings_Opreorder'( Y ) ) ],
% 1.18/1.60 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.18/1.60 'class_Lattices_Olattice'( Y ) ) ],
% 1.18/1.60 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.18/1.60 'class_Orderings_Oorder'( Y ) ) ],
% 1.18/1.60 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 1.18/1.60 Y ) ) ],
% 1.18/1.60 [ 'class_HOL_Ominus'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Ominus'( Y ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'class_HOL_Oord'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Oord'( Y ) ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.18/1.60 ],
% 1.18/1.60 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.18/1.60 ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.18/1.60 ],
% 1.18/1.60 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.18/1.60 ,
% 1.18/1.60 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_HOL_Ominus'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_HOL_Oord'( 'tc_nat' ) ],
% 1.18/1.60 [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_bool' ) ],
% 1.18/1.60 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 1.18/1.60 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 1.18/1.60 [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ],
% 1.18/1.60 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 1.18/1.60 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_bool' ) ],
% 1.18/1.60 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.18/1.60 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.18/1.60 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.18/1.60 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.18/1.60 [ 'class_HOL_Ominus'( 'tc_bool' ) ],
% 1.18/1.60 [ 'class_HOL_Oord'( 'tc_bool' ) ],
% 1.18/1.60 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_Option_Ooption'( X ) ), ~(
% 1.18/1.60 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ],
% 1.18/1.60 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 1.18/1.60 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 1.18/1.60 ] .
% 1.18/1.60
% 1.18/1.60
% 1.18/1.60 percentage equality = 0.242006, percentage horn = 0.842319
% 1.18/1.60 This is a problem with some equality
% 1.18/1.60
% 1.18/1.60
% 1.18/1.60
% 1.18/1.60 Options Used:
% 1.18/1.60
% 1.18/1.60 useres = 1
% 1.18/1.60 useparamod = 1
% 1.18/1.60 useeqrefl = 1
% 1.18/1.60 useeqfact = 1
% 1.18/1.60 usefactor = 1
% 1.18/1.60 usesimpsplitting = 0
% 1.18/1.60 usesimpdemod = 5
% 1.18/1.60 usesimpres = 3
% 1.18/1.60
% 1.18/1.60 resimpinuse = 1000
% 1.18/1.60 resimpclauses = 20000
% 1.18/1.60 substype = eqrewr
% 1.18/1.60 backwardsubs = 1
% 1.18/1.60 selectoldest = 5
% 1.18/1.60
% 1.18/1.60 litorderings [0] = split
% 1.18/1.60 litorderings [1] = extend the termordering, first sorting on arguments
% 1.18/1.60
% 1.18/1.60 termordering = kbo
% 1.18/1.60
% 1.18/1.60 litapriori = 0
% 1.18/1.60 termapriori = 1
% 1.18/1.60 litaposteriori = 0
% 1.18/1.60 termaposteriori = 0
% 1.18/1.60 demodaposteriori = 0
% 1.18/1.60 ordereqreflfact = 0
% 1.18/1.60
% 1.18/1.60 litselect = negord
% 1.18/1.60
% 1.18/1.60 maxweight = 15
% 1.18/1.60 maxdepth = 30000
% 1.18/1.60 maxlength = 115
% 1.18/1.60 maxnrvars = 195
% 1.18/1.60 excuselevel = 1
% 1.18/1.60 increasemaxweight = 1
% 1.18/1.60
% 1.18/1.60 maxselected = 10000000
% 1.18/1.60 maxnrclauses = 10000000
% 1.18/1.60
% 1.18/1.60 showgenerated = 0
% 1.18/1.60 showkept = 0
% 1.18/1.60 showselected = 0
% 1.18/1.60 showdeleted = 0
% 1.18/1.60 showresimp = 1
% 1.18/1.60 showstatus = 2000
% 1.18/1.60
% 1.18/1.60 prologoutput = 1
% 1.18/1.60 nrgoals = 5000000
% 1.18/1.60 totalproof = 1
% 1.18/1.60
% 1.18/1.60 Symbols occurring in the translation:
% 1.18/1.60
% 1.18/1.60 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.18/1.60 . [1, 2] (w:1, o:201, a:1, s:1, b:0),
% 1.18/1.60 ! [4, 1] (w:0, o:119, a:1, s:1, b:0),
% 1.18/1.60 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.18/1.60 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.18/1.60 hAPP [41, 2] (w:1, o:226, a:1, s:1, b:0),
% 1.18/1.60 'c_Lattices_Olower__semilattice' [46, 4] (w:1, o:262, a:1, s:1, b:0)
% 1.18/1.60 ,
% 1.18/1.60 hBOOL [47, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.18/1.60 'class_Orderings_Olinorder' [48, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.18/1.60 'c_lessequals' [49, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.18/1.60 'c_Orderings_Oord__class_Omin' [51, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.18/1.60 'tc_bool' [54, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.18/1.60 'tc_fun' [55, 2] (w:1, o:227, a:1, s:1, b:0),
% 1.18/1.60 'c_Lattices_Oupper__semilattice__class_Osup' [56, 1] (w:1, o:129, a:1
% 1.18/1.60 , s:1, b:0),
% 1.18/1.60 'c_Lattices_Olower__semilattice__class_Oinf' [57, 1] (w:1, o:130, a:1
% 1.18/1.60 , s:1, b:0),
% 1.18/1.60 'c_OrderedGroup_Oab__semigroup__idem__mult' [61, 2] (w:1, o:229, a:1
% 1.18/1.60 , s:1, b:0),
% 1.18/1.60 'class_Orderings_Oorder' [62, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.18/1.60 'c_SetInterval_Oord__class_OatLeastAtMost' [64, 3] (w:1, o:248, a:1
% 1.18/1.60 , s:1, b:0),
% 1.18/1.60 'class_OrderedGroup_Ocomm__monoid__add' [67, 1] (w:1, o:132, a:1, s:1
% 1.18/1.60 , b:0),
% 1.18/1.60 'c_HOL_Oplus__class_Oplus' [68, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.18/1.60 'c_HOL_Ozero__class_Ozero' [70, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.18/1.60 'c_Finite__Set_Ofold__image' [71, 6] (w:1, o:286, a:1, s:1, b:0),
% 1.18/1.60 'c_Finite__Set_Ofinite' [72, 2] (w:1, o:230, a:1, s:1, b:0),
% 1.18/1.60 'c_Orderings_Oord__class_Omax' [73, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.18/1.60 'class_Ring__and__Field_Oidom' [74, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.18/1.60 'class_Int_Onumber__ring' [75, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.18/1.60 'c_HOL_Ominus__class_Ominus' [76, 3] (w:1, o:249, a:1, s:1, b:0),
% 1.18/1.60 'class_OrderedGroup_Ogroup__add' [77, 1] (w:1, o:141, a:1, s:1, b:0)
% 1.18/1.60 ,
% 1.18/1.60 'class_OrderedGroup_Oab__group__add' [78, 1] (w:1, o:142, a:1, s:1
% 1.18/1.60 , b:0),
% 1.18/1.60 'class_Ring__and__Field_Oordered__semiring' [79, 1] (w:1, o:148, a:1
% 1.18/1.60 , s:1, b:0),
% 1.18/1.60 'c_HOL_Oord__class_Oless' [80, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.18/1.60 'c_HOL_Otimes__class_Otimes' [81, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.18/1.60 'class_Ring__and__Field_Oordered__semiring__strict' [82, 1] (w:1, o:
% 1.18/1.60 150, a:1, s:1, b:0),
% 1.18/1.60 'c_fequal' [83, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.18/1.60 'c_COMBC' [84, 4] (w:1, o:263, a:1, s:1, b:0),
% 1.18/1.60 'c_The' [85, 2] (w:1, o:233, a:1, s:1, b:0),
% 1.18/1.60 'class_Ring__and__Field_Ocomm__semiring__1' [86, 1] (w:1, o:152, a:1
% 1.18/1.60 , s:1, b:0),
% 1.18/1.60 'c_Finite__Set_Ofold' [88, 5] (w:1, o:282, a:1, s:1, b:0),
% 1.18/1.60 'c_Finite__Set_Ofold__graph' [89, 5] (w:1, o:283, a:1, s:1, b:0),
% 1.18/1.60 'class_Ring__and__Field_Oordered__ring__strict' [90, 1] (w:1, o:147
% 1.18/1.60 , a:1, s:1, b:0),
% 1.18/1.60 'class_Ring__and__Field_Opordered__ring' [91, 1] (w:1, o:156, a:1, s:
% 1.18/1.60 1, b:0),
% 1.18/1.60 'c_Option_Ooption_OSome' [94, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.18/1.60 'tc_Option_Ooption' [95, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.18/1.60 'c_Fun_Ofun__upd' [96, 5] (w:1, o:284, a:1, s:1, b:0),
% 1.18/1.60 'class_OrderedGroup_Olordered__ab__group__add' [97, 1] (w:1, o:159
% 1.18/1.60 , a:1, s:1, b:0),
% 1.18/1.60 'c_Option_Ooption_ONone' [100, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.18/1.60 'c_COMBK' [101, 3] (w:1, o:250, a:1, s:1, b:0),
% 1.18/1.60 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [102, 1]
% 1.18/1.60 (w:1, o:161, a:1, s:1, b:0),
% 1.18/1.60 'class_HOL_Oord' [103, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.18/1.60 'c_in' [104, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.18/1.60 'c_SetInterval_Oord__class_OlessThan' [106, 2] (w:1, o:231, a:1, s:1
% 1.18/1.60 , b:0),
% 1.18/1.60 'c_Map_Omap__le' [107, 4] (w:1, o:264, a:1, s:1, b:0),
% 1.18/1.60 'class_OrderedGroup_Opordered__comm__monoid__add' [108, 1] (w:1, o:
% 1.18/1.60 163, a:1, s:1, b:0),
% 1.18/1.60 'c_Suc' [109, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.18/1.60 'c_Orderings_Obot__class_Obot' [112, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.18/1.60
% 1.18/1.60 'c_Finite__Set_Osetsum' [113, 4] (w:1, o:265, a:1, s:1, b:0),
% 1.18/1.60 'class_Ring__and__Field_Oring__no__zero__divisors' [114, 1] (w:1, o:
% 1.18/1.60 166, a:1, s:1, b:0),
% 1.18/1.60 'class_Ring__and__Field_Ono__zero__divisors' [115, 1] (w:1, o:146, a:
% 1.18/1.60 1, s:1, b:0),
% 1.18/1.60 'class_Ring__and__Field_Oordered__idom' [116, 1] (w:1, o:153, a:1, s:
% 1.18/1.60 1, b:0),
% 1.18/1.60 'tc_nat' [117, 0] (w:1, o:77, a:1, s:1, b:0),
% 1.18/1.60 'c_Finite__Set_Ocard' [118, 2] (w:1, o:234, a:1, s:1, b:0),
% 1.18/1.60 't_b' [122, 0] (w:1, o:80, a:1, s:1, b:0),
% 1.18/1.60 't_a' [123, 0] (w:1, o:79, a:1, s:1, b:0),
% 1.18/1.60 'c_Option_Ooption_Ooption__case' [124, 5] (w:1, o:285, a:1, s:1, b:0)
% 1.18/1.60 ,
% 1.18/1.60 'c_Map_Orestrict__map' [127, 4] (w:1, o:266, a:1, s:1, b:0),
% 1.18/1.60 'class_Lattices_Olattice' [128, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.18/1.60 'class_Lattices_Olower__semilattice' [129, 1] (w:1, o:168, a:1, s:1
% 1.18/1.60 , b:0),
% 1.18/1.60 'class_Lattices_Oupper__semilattice' [130, 1] (w:1, o:169, a:1, s:1
% 1.18/1.60 , b:0),
% 1.18/1.60 'v_x' [137, 0] (w:1, o:85, a:1, s:1, b:0),
% 1.18/1.60 'c_Set_Oinsert' [138, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.18/1.60 'c_Orderings_Olinorder' [139, 3] (w:1, o:251, a:1, s:1, b:0),
% 1.18/1.60 'class_Ring__and__Field_Omult__zero' [140, 1] (w:1, o:143, a:1, s:1
% 1.18/1.60 , b:0),
% 1.18/1.60 'class_Orderings_Opreorder' [141, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.18/1.60 'c_Map_Odom' [145, 3] (w:1, o:252, a:1, s:1, b:0),
% 1.18/1.60 'class_Ring__and__Field_Oring' [146, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.18/1.60
% 1.18/1.60 'class_OrderedGroup_Opordered__ab__group__add' [147, 1] (w:1, o:173
% 1.18/1.60 , a:1, s:1, b:0),
% 1.18/1.60 'c_Finite__Set_Ofun__left__comm' [148, 3] (w:1, o:253, a:1, s:1, b:0)
% 1.18/1.60 ,
% 1.18/1.60 'c_Finite__Set_Olattice__class_OInf__fin' [149, 1] (w:1, o:174, a:1
% 1.18/1.60 , s:1, b:0),
% 1.18/1.60 'c_Finite__Set_Ofold1' [150, 2] (w:1, o:235, a:1, s:1, b:0),
% 1.18/1.60 'class_OrderedGroup_Opordered__ab__semigroup__add' [151, 1] (w:1, o:
% 1.18/1.60 175, a:1, s:1, b:0),
% 1.18/1.60 'class_Lattices_Odistrib__lattice' [152, 1] (w:1, o:176, a:1, s:1, b:
% 1.18/1.60 0),
% 1.18/1.60 'class_OrderedGroup_Olordered__ab__group__add__join' [153, 1] (w:1
% 1.18/1.60 , o:177, a:1, s:1, b:0),
% 1.18/1.60 'class_Complete__Lattice_Ocomplete__lattice' [154, 1] (w:1, o:178, a:
% 1.18/1.60 1, s:1, b:0),
% 1.18/1.60 'c_Complete__Lattice_OInf__class_OInf' [155, 2] (w:1, o:236, a:1, s:1
% 1.18/1.60 , b:0),
% 1.18/1.60 'class_OrderedGroup_Oab__semigroup__mult' [157, 1] (w:1, o:179, a:1
% 1.18/1.60 , s:1, b:0),
% 1.18/1.60 'class_OrderedGroup_Oab__semigroup__add' [158, 1] (w:1, o:180, a:1
% 1.18/1.60 , s:1, b:0),
% 1.18/1.60 'class_OrderedGroup_Olordered__ab__group__add__meet' [162, 1] (w:1
% 1.18/1.60 , o:181, a:1, s:1, b:0),
% 1.18/1.60 'class_OrderedGroup_Ocomm__monoid__mult' [163, 1] (w:1, o:182, a:1
% 1.18/1.60 , s:1, b:0),
% 1.18/1.60 'c_Finite__Set_Osetprod' [164, 4] (w:1, o:267, a:1, s:1, b:0),
% 1.18/1.60 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [165, 1]
% 1.18/1.60 (w:1, o:183, a:1, s:1, b:0),
% 1.18/1.60 'c_Map_Osko__Map__Xmap__le__def__1__1' [168, 4] (w:1, o:268, a:1, s:1
% 1.18/1.60 , b:0),
% 1.18/1.60 'class_OrderedGroup_Oab__semigroup__idem__mult' [170, 1] (w:1, o:184
% 1.18/1.60 , a:1, s:1, b:0),
% 1.18/1.60 'class_Ring__and__Field_Oordered__semidom' [171, 1] (w:1, o:154, a:1
% 1.18/1.60 , s:1, b:0),
% 1.18/1.60 'c_Complete__Lattice_Ocomplete__lattice' [177, 9] (w:1, o:290, a:1
% 1.18/1.60 , s:1, b:0),
% 1.18/1.60 'class_Ring__and__Field_Osemiring' [178, 1] (w:1, o:185, a:1, s:1, b:
% 1.18/1.60 0),
% 1.18/1.60 'class_Ring__and__Field_Opordered__cancel__semiring' [179, 1] (w:1
% 1.18/1.60 , o:186, a:1, s:1, b:0),
% 1.18/1.60 'class_OrderedGroup_Ocancel__ab__semigroup__add' [180, 1] (w:1, o:187
% 1.18/1.60 , a:1, s:1, b:0),
% 1.18/1.60 'class_OrderedGroup_Ocancel__semigroup__add' [181, 1] (w:1, o:188, a:
% 1.18/1.60 1, s:1, b:0),
% 1.18/1.60 'c_Set_Ovimage' [182, 4] (w:1, o:269, a:1, s:1, b:0),
% 1.18/1.60 'class_Ring__and__Field_Omult__mono' [183, 1] (w:1, o:144, a:1, s:1
% 1.18/1.60 , b:0),
% 1.18/1.60 'class_Ring__and__Field_Omult__mono1' [184, 1] (w:1, o:145, a:1, s:1
% 1.18/1.60 , b:0),
% 1.18/1.60 'c_Complete__Lattice_OSup__class_OSup' [186, 2] (w:1, o:237, a:1, s:1
% 1.18/1.60 , b:0),
% 1.18/1.60 'c_OrderedGroup_Oab__semigroup__mult' [190, 2] (w:1, o:238, a:1, s:1
% 1.18/1.60 , b:0),
% 1.18/1.60 'class_Ring__and__Field_Oordered__comm__semiring__strict' [191, 1]
% 1.18/1.60 (w:1, o:155, a:1, s:1, b:0),
% 1.18/1.60 'class_Ring__and__Field_Opordered__semiring' [192, 1] (w:1, o:189, a:
% 1.18/1.60 1, s:1, b:0),
% 1.18/1.60 'class_OrderedGroup_Omonoid__add' [193, 1] (w:1, o:190, a:1, s:1, b:0
% 1.18/1.60 ),
% 1.18/1.62 'class_Lattices_Obounded__lattice' [196, 1] (w:1, o:191, a:1, s:1, b:
% 1.18/1.62 0),
% 1.18/1.62 'class_Orderings_Obot' [197, 1] (w:1, o:192, a:1, s:1, b:0),
% 1.18/1.62 'c_Nitpick_Ofold__graph_H' [198, 6] (w:1, o:287, a:1, s:1, b:0),
% 1.18/1.62 'class_Ring__and__Field_Ocomm__semiring' [199, 1] (w:1, o:193, a:1
% 1.18/1.62 , s:1, b:0),
% 1.18/1.62 'c_Finite__Set_Olinorder__class_OMax' [200, 1] (w:1, o:194, a:1, s:1
% 1.18/1.62 , b:0),
% 1.18/1.62 'c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1' [201
% 1.18/1.62 , 3] (w:1, o:254, a:1, s:1, b:0),
% 1.18/1.62 'c_Finite__Set_Olinorder__class_OMin' [202, 1] (w:1, o:195, a:1, s:1
% 1.18/1.62 , b:0),
% 1.18/1.62 'c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1' [203
% 1.18/1.62 , 3] (w:1, o:255, a:1, s:1, b:0),
% 1.18/1.62 'c_Option_Oset' [207, 2] (w:1, o:239, a:1, s:1, b:0),
% 1.18/1.62 'c_Map_Omap__add' [208, 4] (w:1, o:270, a:1, s:1, b:0),
% 1.18/1.62 'c_Com_Ocom_OBODY' [210, 1] (w:1, o:196, a:1, s:1, b:0),
% 1.18/1.62 'c_Com_Ocom_OSemi' [213, 2] (w:1, o:240, a:1, s:1, b:0),
% 1.18/1.62 'c_Com_Ocom_OSKIP' [214, 0] (w:1, o:104, a:1, s:1, b:0),
% 1.18/1.62 'c_Hoare__Mirabelle_Ohoare__valids' [218, 3] (w:1, o:256, a:1, s:1
% 1.18/1.62 , b:0),
% 1.18/1.62 'c_Hoare__Mirabelle_Ohoare__derivs' [219, 3] (w:1, o:257, a:1, s:1
% 1.18/1.62 , b:0),
% 1.18/1.62 'c_Natural_Oevalc' [222, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.18/1.62 'c_Nitpick_Osko__Nitpick__XEx1__def__1__3' [226, 2] (w:1, o:228, a:1
% 1.18/1.62 , s:1, b:0),
% 1.18/1.62 'tc_Hoare__Mirabelle_Otriple' [227, 1] (w:1, o:197, a:1, s:1, b:0),
% 1.18/1.62 'c_Hoare__Mirabelle_Otriple_Otriple' [228, 4] (w:1, o:271, a:1, s:1
% 1.18/1.62 , b:0),
% 1.18/1.62 'tc_Com_Ostate' [229, 0] (w:1, o:105, a:1, s:1, b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xescape__2' [230, 4] (w:1, o:273, a:1, s:1
% 1.18/1.62 , b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xescape__1' [231, 4] (w:1, o:272, a:1, s:1
% 1.18/1.62 , b:0),
% 1.18/1.62 'v_c' [235, 0] (w:1, o:107, a:1, s:1, b:0),
% 1.18/1.62 'c_Hoare__Mirabelle_OMGT' [236, 1] (w:1, o:198, a:1, s:1, b:0),
% 1.18/1.62 'c_Finite__Set_Ofold1Set' [239, 3] (w:1, o:258, a:1, s:1, b:0),
% 1.18/1.62 'c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1'
% 1.18/1.62 [240, 3] (w:1, o:259, a:1, s:1, b:0),
% 1.18/1.62 'c_Map_Osko__Map__XdomD__1__1' [241, 4] (w:1, o:274, a:1, s:1, b:0),
% 1.18/1.62
% 1.18/1.62 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1'
% 1.18/1.62 [242, 2] (w:1, o:241, a:1, s:1, b:0),
% 1.18/1.62 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2'
% 1.18/1.62 [243, 2] (w:1, o:242, a:1, s:1, b:0),
% 1.18/1.62 'c_Finite__Set_Olattice_OSup__fin' [244, 3] (w:1, o:260, a:1, s:1, b:
% 1.18/1.62 0),
% 1.18/1.62 'c_Finite__Set_Olattice_OInf__fin' [245, 3] (w:1, o:261, a:1, s:1, b:
% 1.18/1.62 0),
% 1.18/1.62 'class_Ring__and__Field_Ofield' [246, 1] (w:1, o:199, a:1, s:1, b:0)
% 1.18/1.62 ,
% 1.18/1.62 'class_Finite__Set_Ofinite_Ofinite' [249, 1] (w:1, o:200, a:1, s:1
% 1.18/1.62 , b:0),
% 1.18/1.62 'class_HOL_Ominus' [250, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.18/1.62 'c_Option_Othe' [253, 2] (w:1, o:243, a:1, s:1, b:0),
% 1.18/1.62 'c_Set_Ocontents' [254, 2] (w:1, o:232, a:1, s:1, b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3' [258, 6] (w:1
% 1.18/1.62 , o:288, a:1, s:1, b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2' [259, 4] (w:1
% 1.18/1.62 , o:276, a:1, s:1, b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xconseq12__3' [262, 4] (w:1, o:279, a:1, s:
% 1.18/1.62 1, b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xconseq12__2' [263, 4] (w:1, o:278, a:1, s:
% 1.18/1.62 1, b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3' [264, 6] (w:
% 1.18/1.62 1, o:289, a:1, s:1, b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2' [265, 4] (w:
% 1.18/1.62 1, o:281, a:1, s:1, b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1' [266, 4] (w:
% 1.18/1.62 1, o:280, a:1, s:1, b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1' [267, 4] (w:1
% 1.18/1.62 , o:275, a:1, s:1, b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xconseq2__1' [268, 2] (w:1, o:246, a:1, s:1
% 1.18/1.62 , b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xconseq2__2' [269, 2] (w:1, o:247, a:1, s:1
% 1.18/1.62 , b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xconseq12__1' [270, 4] (w:1, o:277, a:1, s:
% 1.18/1.62 1, b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xconseq1__1' [271, 2] (w:1, o:244, a:1, s:1
% 1.18/1.62 , b:0),
% 1.18/1.62 'v_sko__Hoare__Mirabelle__Xconseq1__2' [272, 2] (w:1, o:245, a:1, s:1
% 1.18/1.62 , b:0),
% 1.18/1.62 'c_Com_Obody' [274, 0] (w:1, o:103, a:1, s:1, b:0),
% 1.18/1.62 'tc_Com_Ocom' [275, 0] (w:1, o:111, a:1, s:1, b:0),
% 1.18/1.62 'tc_Com_Opname' [277, 0] (w:1, o:112, a:1, s:1, b:0),
% 1.18/1.62 'v_G' [286, 0] (w:1, o:115, a:1, s:1, b:0).
% 1.18/1.62
% 1.18/1.62
% 1.18/1.62 Starting Search:
% 1.18/1.62
% 1.18/1.62
% 1.18/1.62 Bliksems!, er is een bewijs:
% 1.18/1.62 % SZS status Unsatisfiable
% 1.18/1.62 % SZS output start Refutation
% 1.18/1.62
% 1.18/1.62 clause( 872, [ hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP' )
% 1.18/1.62 , X ), X ) ) ] )
% 1.18/1.62 .
% 1.18/1.62 clause( 891, [] )
% 1.18/1.62 .
% 1.18/1.62
% 1.18/1.62
% 1.18/1.62 % SZS output end Refutation
% 1.18/1.62 found a proof!
% 1.18/1.62
% 1.18/1.62 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.18/1.62
% 1.18/1.62 initialclauses(
% 1.18/1.62 [ clause( 893, [ ~( =( hAPP( hAPP( X, Y ), Z ), Y ) ), ~(
% 1.18/1.62 'c_Lattices_Olower__semilattice'( T, U, X, W ) ), hBOOL( hAPP( hAPP( T, Y
% 1.18/1.62 ), Z ) ) ] )
% 1.18/1.62 , clause( 894, [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( hBOOL( hAPP( hAPP( T,
% 1.18/1.62 Z ), Y ) ) ), ~( 'c_Lattices_Olower__semilattice'( T, U, X, W ) ) ] )
% 1.18/1.62 , clause( 895, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.62 ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ) )
% 1.18/1.62 ] )
% 1.18/1.62 , clause( 896, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.62 ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), T ), Z ) ) ) )
% 1.18/1.62 ] )
% 1.18/1.62 , clause( 897, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y )
% 1.18/1.62 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 898, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y )
% 1.18/1.62 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 899, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y )
% 1.18/1.62 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 900, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y )
% 1.18/1.62 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 901, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.62 ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ) )
% 1.18/1.62 ] )
% 1.18/1.62 , clause( 902, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.62 ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), T ), Z ) ) ) )
% 1.18/1.62 ] )
% 1.18/1.62 , clause( 903, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.62 X, 'tc_bool' ) ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), T ), Y ) ) ) ] )
% 1.18/1.62 , clause( 904, [ ~( =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.62 X, 'tc_bool' ) ), Z ), T ) ) ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), T ), Y ) ) ] )
% 1.18/1.62 , clause( 905, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.18/1.62 'c_OrderedGroup_Oab__semigroup__idem__mult'(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), X ) ] )
% 1.18/1.62 , clause( 906, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.62 ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, X ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, U, X ) ) ) ) ] )
% 1.18/1.62 , clause( 907, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.62 ), T ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( T, Y, X ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( U, Z, X ) ) ) ) ] )
% 1.18/1.62 , clause( 908, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), T ), Y ) ) ) ] )
% 1.18/1.62 , clause( 909, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Ofold__image'(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.18/1.62 , T ) ), 'c_Finite__Set_Ofold__image'( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.62 , 'c_HOL_Ozero__class_Ozero'( X ), U, X, T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Ofold__image'(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( T,
% 1.18/1.62 'tc_bool' ) ), Z ), U ), X, T ) ), 'c_Finite__Set_Ofold__image'(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( T,
% 1.18/1.62 'tc_bool' ) ), Z ), U ), X, T ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) )
% 1.18/1.62 , ~( 'c_Finite__Set_Ofinite'( Z, T ) ) ] )
% 1.18/1.62 , clause( 910, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.62 Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), T ), Z ) ) ) ) ] )
% 1.18/1.62 , clause( 911, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.18/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 1.18/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 912, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 913, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 914, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 915, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 916, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.18/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ] )
% 1.18/1.62 , clause( 917, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.18/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ] )
% 1.18/1.62 , clause( 918, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.62 , T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ] )
% 1.18/1.62 , clause( 919, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.62 , T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ] )
% 1.18/1.62 , clause( 920, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.18/1.62 'class_Int_Onumber__ring'( X ) ), ~( =( Y, hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), =( Z,
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 921, [ =( 'c_The'( hAPP( 'c_COMBC'( 'c_fequal'( X ), X, X,
% 1.18/1.62 'tc_bool' ), Y ), X ), Y ) ] )
% 1.18/1.62 , clause( 922, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 923, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 924, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 925, [ =( 'c_Finite__Set_Ofold'( X, Y, Z, T, U ), 'c_The'(
% 1.18/1.62 'c_Finite__Set_Ofold__graph'( X, Y, Z, T, U ), U ) ) ] )
% 1.18/1.62 , clause( 926, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ) ] )
% 1.18/1.62 , clause( 927, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), T ) ), U ) ), W ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ) ),
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ] )
% 1.18/1.62 , clause( 928, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ),
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ), W ) ) ) ] )
% 1.18/1.62 , clause( 929, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ) ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ) ),
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ] )
% 1.18/1.62 , clause( 930, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ),
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ) ) ) ) ] )
% 1.18/1.62 , clause( 931, [ ~( =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ), T
% 1.18/1.62 ) ) ), =( Y, U ), =( hAPP( 'c_Fun_Ofun__upd'( X, U, hAPP(
% 1.18/1.62 'c_Option_Ooption_OSome'( Z ), W ), V0, 'tc_Option_Ooption'( Z ) ), Y ),
% 1.18/1.62 hAPP( 'c_Option_Ooption_OSome'( Z ), T ) ) ] )
% 1.18/1.62 , clause( 932, [ ~( =( hAPP( 'c_Fun_Ofun__upd'( X, Y, hAPP(
% 1.18/1.62 'c_Option_Ooption_OSome'( Z ), T ), U, 'tc_Option_Ooption'( Z ) ), W ),
% 1.18/1.62 hAPP( 'c_Option_Ooption_OSome'( Z ), V0 ) ) ), =( hAPP( X, W ), hAPP(
% 1.18/1.62 'c_Option_Ooption_OSome'( Z ), V0 ) ), =( T, V0 ) ] )
% 1.18/1.62 , clause( 933, [ ~( =( hAPP( 'c_Fun_Ofun__upd'( X, Y, hAPP(
% 1.18/1.62 'c_Option_Ooption_OSome'( Z ), T ), U, 'tc_Option_Ooption'( Z ) ), W ),
% 1.18/1.62 hAPP( 'c_Option_Ooption_OSome'( Z ), V0 ) ) ), =( hAPP( X, W ), hAPP(
% 1.18/1.62 'c_Option_Ooption_OSome'( Z ), V0 ) ), =( W, Y ) ] )
% 1.18/1.62 , clause( 934, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 935, [ ~( =( 'c_Fun_Ofun__upd'( X, Y, hAPP(
% 1.18/1.62 'c_Option_Ooption_OSome'( Z ), T ), U, 'tc_Option_Ooption'( Z ) ),
% 1.18/1.62 'c_COMBK'( 'c_Option_Ooption_ONone'( Z ), 'tc_Option_Ooption'( Z ), U ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 936, [ ~(
% 1.18/1.62 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.18/1.62 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z
% 1.18/1.62 ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.62 , T ) ) ) ] )
% 1.18/1.62 , clause( 937, [ ~(
% 1.18/1.62 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.18/1.62 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z
% 1.18/1.62 ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.62 , Z ) ) ) ] )
% 1.18/1.62 , clause( 938, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 939, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 940, [ ~( 'class_HOL_Oord'( X ) ), hBOOL( hAPP( hAPP( 'c_in'( X )
% 1.18/1.62 , Y ), 'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 941, [ ~( 'class_HOL_Oord'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.18/1.62 X ), Y ), 'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ) ) ] )
% 1.18/1.62 , clause( 942, [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( hBOOL( hAPP( hAPP( T,
% 1.18/1.62 Y ), Z ) ) ), ~( 'c_Lattices_Olower__semilattice'( T, U, X, W ) ) ] )
% 1.18/1.62 , clause( 943, [ 'c_Map_Omap__le'( 'c_Fun_Ofun__upd'( X, Y, Z, T,
% 1.18/1.62 'tc_Option_Ooption'( U ) ), 'c_Fun_Ofun__upd'( W, Y, Z, T,
% 1.18/1.62 'tc_Option_Ooption'( U ) ), T, U ), ~( 'c_Map_Omap__le'( X, W, T, U ) ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 944, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.18/1.62 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), =( Z,
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 945, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.18/1.62 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), =( Y,
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 946, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.62 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.62 ) ) ] )
% 1.18/1.62 , clause( 947, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 1.18/1.62 , clause( 948, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 1.18/1.62 , clause( 949, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), Z ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ) ) ) ) ] )
% 1.18/1.62 , clause( 950, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ) ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), T ), U ) ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ] )
% 1.18/1.62 , clause( 951, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), Z ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ), W ) ) ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 952, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), T ) ), U ) ), W ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), T ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ] )
% 1.18/1.62 , clause( 953, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =(
% 1.18/1.62 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y,
% 1.18/1.62 'tc_bool' ) ), Z ), T ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.18/1.62 'tc_bool' ) ) ) ), ~( 'c_Finite__Set_Ofinite'( T, Y ) ), ~(
% 1.18/1.62 'c_Finite__Set_Ofinite'( Z, Y ) ), =( 'c_Finite__Set_Osetsum'( U, hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y,
% 1.18/1.62 'tc_bool' ) ), Z ), T ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), 'c_Finite__Set_Osetsum'( U, Z, Y, X ) ), 'c_Finite__Set_Osetsum'( U
% 1.18/1.62 , T, Y, X ) ) ) ] )
% 1.18/1.62 , clause( 954, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( T, U, X ) ) ), hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ] )
% 1.18/1.62 , clause( 955, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.62 T ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), T ), Y ) ), Z ) ) ) ] )
% 1.18/1.62 , clause( 956, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.18/1.62 'c_OrderedGroup_Oab__semigroup__idem__mult'(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), X ) ] )
% 1.18/1.62 , clause( 957, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 1.18/1.62 ), ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.62 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 958, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 1.18/1.62 ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.62 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 959, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 1.18/1.62 ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.62 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 960, [ =( 'c_Fun_Ofun__upd'( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ),
% 1.18/1.62 W, V0, T, U ), 'c_Fun_Ofun__upd'( 'c_Fun_Ofun__upd'( X, W, V0, T, U ), Y
% 1.18/1.62 , Z, T, U ) ), =( Y, W ) ] )
% 1.18/1.62 , clause( 961, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 962, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.62 ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 963, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.62 ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 964, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 965, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ] )
% 1.18/1.62 , clause( 966, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ] )
% 1.18/1.62 , clause( 967, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.18/1.62 , clause( 968, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 969, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X
% 1.18/1.62 , 'tc_bool' ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Finite__Set_Ocard'( Y, X ) ),
% 1.18/1.62 'c_Finite__Set_Ocard'( Z, X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z,
% 1.18/1.62 X ) ) ] )
% 1.18/1.62 , clause( 970, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.62 ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), T ), Y ) ), Z ) ) )
% 1.18/1.62 ] )
% 1.18/1.62 , clause( 971, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.62 ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ), Z ) ) )
% 1.18/1.62 ] )
% 1.18/1.62 , clause( 972, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.18/1.62 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 973, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.18/1.62 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 974, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.18/1.62 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 975, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.18/1.62 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 976, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.62 ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), T ), Y ) ), Z ) ) )
% 1.18/1.62 ] )
% 1.18/1.62 , clause( 977, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.62 ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ), Z ) ) )
% 1.18/1.62 ] )
% 1.18/1.62 , clause( 978, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), T ), Z ) ) ) ) ] )
% 1.18/1.62 , clause( 979, [ ~( hBOOL( hAPP( X, 'c_Option_Ooption_Ooption__case'( Y, Z
% 1.18/1.62 , hAPP( 'c_Option_Ooption_OSome'( 't_b' ), T ), 't_a', 't_b' ) ) ) ),
% 1.18/1.62 hBOOL( hAPP( X, hAPP( Z, T ) ) ) ] )
% 1.18/1.62 , clause( 980, [ ~( hBOOL( hAPP( X, 'c_Option_Ooption_Ooption__case'( Y, Z
% 1.18/1.62 , hAPP( 'c_Option_Ooption_OSome'( 't_b' ), T ), 't_a', 't_b' ) ) ) ),
% 1.18/1.62 hBOOL( hAPP( X, hAPP( Z, T ) ) ) ] )
% 1.18/1.62 , clause( 981, [ =( 'c_Map_Orestrict__map'( 'c_Fun_Ofun__upd'( X, Y, Z, T,
% 1.18/1.62 'tc_Option_Ooption'( U ) ), W, T, U ), 'c_Map_Orestrict__map'( X, W, T, U
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), W ) ) ] )
% 1.18/1.62 , clause( 982, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 983, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 984, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 985, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 986, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.62 X, 'tc_bool' ) ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 987, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.62 X, 'tc_bool' ) ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Z ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.62 X, 'tc_bool' ) ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 988, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.18/1.62 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 989, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.18/1.62 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ) ) ] )
% 1.18/1.62 , clause( 990, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), T ), Y ) ), Z ) ) ) ] )
% 1.18/1.62 , clause( 991, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.18/1.62 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U )
% 1.18/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), =( Z, U ), =( Y, T ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 992, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.18/1.62 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U )
% 1.18/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), =( Z, U ), =( Y, T ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 993, [ =( 'c_Map_Orestrict__map'( 'c_Map_Orestrict__map'( X, Y, Z
% 1.18/1.62 , T ), U, Z, T ), 'c_Map_Orestrict__map'( X, hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.18/1.62 , Y ), U ), Z, T ) ) ] )
% 1.18/1.62 , clause( 994, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.18/1.62 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 995, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.18/1.62 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 996, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.62 'c_Finite__Set_Osetsum'( Y, Z, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.62 , 'c_Finite__Set_Ofinite'( Z, T ) ] )
% 1.18/1.62 , clause( 997, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.62 'c_Finite__Set_Osetsum'( Y, Z, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.62 , 'c_Finite__Set_Ofinite'( Z, T ) ] )
% 1.18/1.62 , clause( 998, [ =( X, Y ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.62 'tc_nat' ), X ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.62 'tc_nat' ), X ), 'c_Suc'( Y ) ) ) ) ] )
% 1.18/1.62 , clause( 999, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.62 'tc_nat' ), Y ), 'c_Suc'( X ) ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ) ] )
% 1.18/1.62 , clause( 1000, [ =( X, Y ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'( Y ) ) ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ] )
% 1.18/1.62 , clause( 1001, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 1.18/1.62 , clause( 1002, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ] )
% 1.18/1.62 , clause( 1003, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ] )
% 1.18/1.62 , clause( 1004, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ] )
% 1.18/1.62 , clause( 1005, [ =( hAPP( 'c_Map_Orestrict__map'( 'c_COMBK'(
% 1.18/1.62 'c_Option_Ooption_ONone'( X ), 'tc_Option_Ooption'( X ), 't_a' ), Y,
% 1.18/1.62 't_a', X ), 'v_x' ), 'c_Option_Ooption_ONone'( X ) ) ] )
% 1.18/1.62 , clause( 1006, [ =( 'c_Map_Orestrict__map'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.62 Y ), Z ), T ), Y, U ), 'c_Fun_Ofun__upd'( 'c_Map_Orestrict__map'( X, T, Y
% 1.18/1.62 , U ), Z, hAPP( X, Z ), Y, 'tc_Option_Ooption'( U ) ) ) ] )
% 1.18/1.62 , clause( 1007, [ 'c_Orderings_Olinorder'( 'c_COMBC'( X, Y, Y, 'tc_bool' )
% 1.18/1.62 , 'c_COMBC'( Z, Y, Y, 'tc_bool' ), Y ), ~( 'c_Orderings_Olinorder'( X, Z
% 1.18/1.62 , Y ) ) ] )
% 1.18/1.62 , clause( 1008, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.62 ] )
% 1.18/1.62 , clause( 1009, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 1010, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 1.18/1.62 ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 1011, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 1.18/1.62 ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.62 ] )
% 1.18/1.62 , clause( 1012, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 1013, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 1014, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.62 ] )
% 1.18/1.62 , clause( 1015, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Y ), T ), 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.18/1.62 , clause( 1016, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ), T ),
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), T ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Z ), T ), 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.18/1.62 , clause( 1017, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.18/1.62 'c_Finite__Set_Ofold'( 'c_Lattices_Olower__semilattice__class_Oinf'( X )
% 1.18/1.62 , Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ), X, X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ),
% 1.18/1.62 'c_Finite__Set_Ofold'( 'c_Lattices_Olower__semilattice__class_Oinf'( X )
% 1.18/1.62 , Y, T, X, X ) ) ), ~( 'c_Finite__Set_Ofinite'( T, X ) ) ] )
% 1.18/1.62 , clause( 1018, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.62 'c_Finite__Set_Osetsum'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.18/1.62 'tc_bool' ) ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 1019, [ =( 'c_Fun_Ofun__upd'( 'c_Fun_Ofun__upd'( X, Y, Z, T, U )
% 1.18/1.62 , Y, W, T, U ), 'c_Fun_Ofun__upd'( X, Y, W, T, U ) ) ] )
% 1.18/1.62 , clause( 1020, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( T, U, 'tc_fun'( X, 'tc_bool' ) ) ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), U ), Z ) )
% 1.18/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y )
% 1.18/1.62 , T ) ) ) ] )
% 1.18/1.62 , clause( 1021, [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ), hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ) ] )
% 1.18/1.62 , clause( 1022, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), T ), Z ), 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.18/1.62 , clause( 1023, [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.62 ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1024, [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'(
% 1.18/1.62 X, 'tc_bool' ) ), Y ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1025, [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.18/1.62 ), X ), X ) ) ) ] )
% 1.18/1.62 , clause( 1026, [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.18/1.62 ), X ), X ) ) ) ] )
% 1.18/1.62 , clause( 1027, [ ~( 'class_HOL_Oord'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( 'tc_fun'( Y, X ) ), Z ), T ) ), hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( 'tc_fun'( Y, X ) ), T ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( 'tc_fun'( Y, X ) ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1028, [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1029, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1030, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1031, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), Y ) ] )
% 1.18/1.62 , clause( 1032, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Y ), Y ) ] )
% 1.18/1.62 , clause( 1033, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.18/1.62 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1034, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 X ), T ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1035, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 X ), T ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1036, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool' )
% 1.18/1.62 , 'tc_bool' ), Y ) ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ), 'tc_bool' ), Z ) ) ) ) ] )
% 1.18/1.62 , clause( 1037, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool' ),
% 1.18/1.62 'tc_bool' ), Y ) ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ), 'tc_bool' ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1038, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Y ), Z ) ), hAPP(
% 1.18/1.62 hAPP( X, Y ), Z ) ), ~( 'c_OrderedGroup_Oab__semigroup__idem__mult'( X, T
% 1.18/1.62 ) ) ] )
% 1.18/1.62 , clause( 1039, [ =( hAPP( hAPP( X, Y ), Y ), Y ), ~(
% 1.18/1.62 'c_OrderedGroup_Oab__semigroup__idem__mult'( X, Z ) ) ] )
% 1.18/1.62 , clause( 1040, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), =( Z, Y ) ] )
% 1.18/1.62 , clause( 1041, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ] )
% 1.18/1.62 , clause( 1042, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.62 'c_Finite__Set_Osetsum'( 'c_COMBK'( 'c_HOL_Ozero__class_Ozero'( X ), X, Y
% 1.18/1.62 ), Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 1043, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.62 , 'c_Finite__Set_Ocard'( X, Y ) ), 'c_Finite__Set_Ocard'( Z, Y ) ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.62 , X ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ] )
% 1.18/1.62 , clause( 1044, [ =( 'c_Map_Odom'( 'c_Map_Orestrict__map'( X, Y, Z, T ), Z
% 1.18/1.62 , T ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.62 Z, 'tc_bool' ) ), 'c_Map_Odom'( X, Z, T ) ), Y ) ) ] )
% 1.18/1.62 , clause( 1045, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.18/1.62 , Z ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1046, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.18/1.62 , Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1047, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y )
% 1.18/1.62 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1048, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y )
% 1.18/1.62 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1049, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y )
% 1.18/1.62 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1050, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), U ), Z ) ), W ) ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.62 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W ) ] )
% 1.18/1.62 , clause( 1051, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), U ), Z ) ), W ) ) ), =( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ) ) ] )
% 1.18/1.62 , clause( 1052, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( T, Y, X
% 1.18/1.62 ) ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ) ] )
% 1.18/1.62 , clause( 1053, [ =( hAPP( hAPP( X, Y ), Y ), Y ), ~(
% 1.18/1.62 'c_Lattices_Olower__semilattice'( Z, T, X, U ) ) ] )
% 1.18/1.62 , clause( 1054, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP(
% 1.18/1.62 hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ) ), ~(
% 1.18/1.62 'c_Lattices_Olower__semilattice'( U, W, X, V0 ) ) ] )
% 1.18/1.62 , clause( 1055, [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ),
% 1.18/1.62 ~( 'c_Lattices_Olower__semilattice'( T, U, X, W ) ) ] )
% 1.18/1.62 , clause( 1056, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Y ), Z ) ), hAPP(
% 1.18/1.62 hAPP( X, Y ), Z ) ), ~( 'c_Lattices_Olower__semilattice'( T, U, X, W ) )
% 1.18/1.62 ] )
% 1.18/1.62 , clause( 1057, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 1.18/1.62 hAPP( X, Z ), hAPP( hAPP( X, Y ), T ) ) ), ~(
% 1.18/1.62 'c_Lattices_Olower__semilattice'( U, W, X, V0 ) ) ] )
% 1.18/1.62 , clause( 1058, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.18/1.62 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z,
% 1.18/1.62 'tc_bool' ) ), T ), U ), Z, X ) ), 'c_Finite__Set_Osetsum'( Y, hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.18/1.62 , T ), U ), Z, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.62 'c_Finite__Set_Osetsum'( Y, T, Z, X ) ), 'c_Finite__Set_Osetsum'( Y, U, Z
% 1.18/1.62 , X ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ), ~(
% 1.18/1.62 'c_Finite__Set_Ofinite'( T, Z ) ) ] )
% 1.18/1.62 , clause( 1059, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.62 ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z )
% 1.18/1.62 , U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T )
% 1.18/1.62 ) ) ] )
% 1.18/1.62 , clause( 1060, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y )
% 1.18/1.62 , Z ) ), Y ) ) ] )
% 1.18/1.62 , clause( 1061, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y )
% 1.18/1.62 , Z ) ), Z ) ) ] )
% 1.18/1.62 , clause( 1062, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X )
% 1.18/1.62 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1063, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X )
% 1.18/1.62 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1064, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X )
% 1.18/1.62 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1065, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ) ) ] )
% 1.18/1.62 , clause( 1066, [ =( 'c_Option_Ooption_Ooption__case'( X, Y, hAPP(
% 1.18/1.62 'c_Option_Ooption_OSome'( Z ), T ), U, Z ), hAPP( Y, T ) ) ] )
% 1.18/1.62 , clause( 1067, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.18/1.62 , =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), T, X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), 'c_HOL_Ominus__class_Ominus'( Y, T,
% 1.18/1.62 X ) ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ) ) ] )
% 1.18/1.62 , clause( 1068, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1069, [ =( 'c_Finite__Set_Ofold'( X, Y, hAPP( hAPP(
% 1.18/1.62 'c_Set_Oinsert'( Z ), T ), U ), Z, Z ), hAPP( hAPP( X, T ),
% 1.18/1.62 'c_Finite__Set_Ofold'( X, Y, U, Z, Z ) ) ), ~( 'c_Finite__Set_Ofinite'( U
% 1.18/1.62 , Z ) ), ~( 'c_Lattices_Olower__semilattice'( W, V0, X, Z ) ) ] )
% 1.18/1.62 , clause( 1070, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 1.18/1.62 hAPP( X, Z ), hAPP( hAPP( X, Y ), T ) ) ), ~(
% 1.18/1.62 'c_Finite__Set_Ofun__left__comm'( X, U, W ) ) ] )
% 1.18/1.62 , clause( 1071, [ =( X, Y ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'(
% 1.18/1.62 Z, T, U, W, V0 ), X ) ) ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'(
% 1.18/1.62 Z, T, U, W, V0 ), Y ) ) ), ~( 'c_Finite__Set_Ofun__left__comm'( Z, W, V0
% 1.18/1.62 ) ) ] )
% 1.18/1.62 , clause( 1072, [ ~(
% 1.18/1.62 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.18/1.62 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1073, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1074, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.18/1.62 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1075, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.18/1.62 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1076, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.62 'c_Finite__Set_Osetsum'( Y, Z, T, X ), 'c_Finite__Set_Ofold__image'(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.18/1.62 , T ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ) ] )
% 1.18/1.62 , clause( 1077, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.62 ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), Y ), Y ) ) ) ) ] )
% 1.18/1.62 , clause( 1078, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1079, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ) ] )
% 1.18/1.62 , clause( 1080, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.18/1.62 ), Z ), Y ) ] )
% 1.18/1.62 , clause( 1081, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.18/1.62 'c_Finite__Set_Olattice__class_OInf__fin'( X ), 'c_Finite__Set_Ofold1'(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), X ) ) ] )
% 1.18/1.62 , clause( 1082, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1083, [ 'c_Finite__Set_Ofinite'( X, Y ), ~( hBOOL( hAPP(
% 1.18/1.62 'c_Finite__Set_Ofold__graph'( Z, T, X, Y, U ), W ) ) ) ] )
% 1.18/1.62 , clause( 1084, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.18/1.62 'c_OrderedGroup_Oab__semigroup__idem__mult'(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), X ) ] )
% 1.18/1.62 , clause( 1085, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1086, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.62 X, 'tc_bool' ) ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1087, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1088, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1089, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 1090, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.18/1.62 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 1091, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.18/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 1092, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 1093, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'(
% 1.18/1.62 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1094, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'(
% 1.18/1.62 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1095, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.18/1.62 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1096, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.18/1.62 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1097, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ),
% 1.18/1.62 'c_Complete__Lattice_OInf__class_OInf'( Z, X ) ), 'c_Finite__Set_Ofold'(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y, Z, X, X ) ), ~(
% 1.18/1.62 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.18/1.62 , clause( 1098, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.18/1.62 ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.62 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1099, [ =( X, Y ), ~( =( hAPP( 'c_Fun_Ofun__upd'( Z, T, hAPP(
% 1.18/1.62 'c_Option_Ooption_OSome'( U ), X ), W, 'tc_Option_Ooption'( U ) ), T ),
% 1.18/1.62 hAPP( 'c_Option_Ooption_OSome'( U ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1100, [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1101, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X
% 1.18/1.62 , 'tc_bool' ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), T ), Z ) ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1102, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1103, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ),
% 1.18/1.62 'c_Finite__Set_Ofun__left__comm'( 'c_HOL_Otimes__class_Otimes'( X ), X, X
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1104, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), Z ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1105, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ) ] )
% 1.18/1.62 , clause( 1106, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), Y ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Z ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1107, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), Y ), Z ) ), T ) ) ] )
% 1.18/1.62 , clause( 1108, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1109, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1110, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1111, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1112, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), Y ), Z ) ), T ) ) ] )
% 1.18/1.62 , clause( 1113, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), Y ), T ) ), Z ) ) ] )
% 1.18/1.62 , clause( 1114, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1115, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1116, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.18/1.62 'c_Finite__Set_Ofun__left__comm'( 'c_HOL_Oplus__class_Oplus'( X ), X, X )
% 1.18/1.62 ] )
% 1.18/1.62 , clause( 1117, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.18/1.62 'c_Orderings_Olinorder'( 'c_COMBC'( 'c_lessequals'( X ), X, X, 'tc_bool'
% 1.18/1.62 ), 'c_COMBC'( 'c_HOL_Oord__class_Oless'( X ), X, X, 'tc_bool' ), X ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 1118, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ] )
% 1.18/1.62 , clause( 1119, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.18/1.62 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ),
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ) ) ] )
% 1.18/1.62 , clause( 1120, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), Y ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1121, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ) ] )
% 1.18/1.62 , clause( 1122, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), Z ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Z ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1123, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.18/1.62 , =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), T, X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), 'c_HOL_Ominus__class_Ominus'( Y, T,
% 1.18/1.62 X ) ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ) ) ] )
% 1.18/1.62 , clause( 1124, [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP(
% 1.18/1.62 hAPP( X, W ), U ) ) ] )
% 1.18/1.62 , clause( 1125, [ =( hAPP( 'c_COMBK'( X, Y, Z ), T ), X ) ] )
% 1.18/1.62 , clause( 1126, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 1127, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1128, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Y ) ) ] )
% 1.18/1.62 , clause( 1129, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Z ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1130, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 1131, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1132, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 1133, [ ~( 'class_HOL_Oord'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( 'tc_fun'( Y, X ) ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( 'tc_fun'( Y, X ) ), T ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1134, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1135, [ ~( hBOOL( hAPP( X, 'c_Option_Ooption_Ooption__case'( Y, Z
% 1.18/1.62 , 'c_Option_Ooption_ONone'( 't_b' ), 't_a', 't_b' ) ) ) ), hBOOL( hAPP( X
% 1.18/1.62 , Y ) ) ] )
% 1.18/1.62 , clause( 1136, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'(
% 1.18/1.62 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1137, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'(
% 1.18/1.62 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1138, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.18/1.62 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1139, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.18/1.62 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1140, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1141, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1142, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'(
% 1.18/1.62 Z, 'tc_bool' ) ), Y ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 'tc_fun'( Z, 'tc_bool' ) ), X ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1143, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.62 , X ), Y ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y
% 1.18/1.62 ), X ) ), =( Y, X ) ] )
% 1.18/1.62 , clause( 1144, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'(
% 1.18/1.62 Z, 'tc_bool' ) ), Y ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 'tc_fun'( Z, 'tc_bool' ) ), X ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1145, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 1146, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.62 , X ), Y ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y
% 1.18/1.62 ), X ) ), =( Y, X ) ] )
% 1.18/1.62 , clause( 1147, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1148, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), =( Z, Y ) ] )
% 1.18/1.62 , clause( 1149, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1150, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Z ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1151, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Z, Y ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 1152, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 1153, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetprod'(
% 1.18/1.62 Y, hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z
% 1.18/1.62 , 'tc_bool' ) ), T ), U ), Z, X ) ), 'c_Finite__Set_Osetprod'( Y, hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z,
% 1.18/1.62 'tc_bool' ) ), T ), U ), Z, X ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetprod'( Y, T, Z, X )
% 1.18/1.62 ), 'c_Finite__Set_Osetprod'( Y, U, Z, X ) ) ), ~(
% 1.18/1.62 'c_Finite__Set_Ofinite'( U, Z ) ), ~( 'c_Finite__Set_Ofinite'( T, Z ) ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 1154, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 1155, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.18/1.62 , Z, X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1156, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Y ), Y ), Y ) ] )
% 1.18/1.62 , clause( 1157, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), ~(
% 1.18/1.62 =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y
% 1.18/1.62 , 'tc_bool' ) ), Z ), T ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.18/1.62 'tc_bool' ) ) ) ), ~( 'c_Finite__Set_Ofinite'( T, Y ) ), ~(
% 1.18/1.62 'c_Finite__Set_Ofinite'( Z, Y ) ), =( 'c_Finite__Set_Osetprod'( U, hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y,
% 1.18/1.62 'tc_bool' ) ), Z ), T ), Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), 'c_Finite__Set_Osetprod'( U, Z, Y, X ) ), 'c_Finite__Set_Osetprod'(
% 1.18/1.62 U, T, Y, X ) ) ) ] )
% 1.18/1.62 , clause( 1158, [ ~(
% 1.18/1.62 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1159, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), Y ) ] )
% 1.18/1.62 , clause( 1160, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1161, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1162, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1163, [ ~( 'class_HOL_Oord'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( 'tc_fun'( Y, X ) ), Z ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( 'tc_fun'( Y, X ) ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1164, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1165, [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1166, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), Y ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1167, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 1.18/1.62 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ),
% 1.18/1.62 Z ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ] )
% 1.18/1.62 , clause( 1168, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), Z ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1169, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), Z ), Z ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1170, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), Z ), Y ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Z ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1171, [ ~( =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), Z ), Z ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Y ), Z ) ) ] )
% 1.18/1.62 , clause( 1172, [ ~( =( hAPP( X, 'c_Map_Osko__Map__Xmap__le__def__1__1'( X
% 1.18/1.62 , Y, Z, T ) ), hAPP( Y, 'c_Map_Osko__Map__Xmap__le__def__1__1'( X, Y, Z,
% 1.18/1.62 T ) ) ) ), 'c_Map_Omap__le'( X, Y, Z, T ) ] )
% 1.18/1.62 , clause( 1173, [ =( 'c_Option_Ooption_Ooption__case'( X, Y,
% 1.18/1.62 'c_Option_Ooption_ONone'( Z ), T, Z ), X ) ] )
% 1.18/1.62 , clause( 1174, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.62 Y, Z, X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 1175, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.62 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1176, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.62 'c_Finite__Set_Osetsum'( Y, hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.18/1.62 , T ), U ), Z, X ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y, T, Z, X ) )
% 1.18/1.62 , 'c_Finite__Set_Osetsum'( Y, U, Z, X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.18/1.62 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z,
% 1.18/1.62 'tc_bool' ) ), T ), U ), Z, X ), X ) ), ~( 'c_Finite__Set_Ofinite'( U, Z
% 1.18/1.62 ) ), ~( 'c_Finite__Set_Ofinite'( T, Z ) ) ] )
% 1.18/1.62 , clause( 1177, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.62 , X ), 'c_Suc'( X ) ) ) ] )
% 1.18/1.62 , clause( 1178, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.62 , X ), 'c_Suc'( X ) ) ) ] )
% 1.18/1.62 , clause( 1179, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.62 , 'c_Suc'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.62 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.62 'tc_nat' ), X ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1180, [ ~(
% 1.18/1.62 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) )
% 1.18/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1181, [ ~(
% 1.18/1.62 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T
% 1.18/1.62 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ] )
% 1.18/1.62 , clause( 1182, [ ~(
% 1.18/1.62 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) )
% 1.18/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1183, [ ~(
% 1.18/1.62 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y
% 1.18/1.62 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ] )
% 1.18/1.62 , clause( 1184, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1185, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1186, [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( X, Z ), Y ) ) ), ~( 'c_Orderings_Olinorder'( T, X, U ) ) ] )
% 1.18/1.62 , clause( 1187, [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( T, Z ), Y ) ) ), ~( 'c_Orderings_Olinorder'( T, X, U ) ) ] )
% 1.18/1.62 , clause( 1188, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( T, Z
% 1.18/1.62 ), Y ) ), ~( 'c_Orderings_Olinorder'( X, T, U ) ) ] )
% 1.18/1.62 , clause( 1189, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Z
% 1.18/1.62 ), Y ) ), ~( 'c_Orderings_Olinorder'( X, T, U ) ) ] )
% 1.18/1.62 , clause( 1190, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( T, Z
% 1.18/1.62 ), Y ) ), ~( 'c_Orderings_Olinorder'( T, X, U ) ) ] )
% 1.18/1.62 , clause( 1191, [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( T, Z ), Y ) ) ), ~( 'c_Orderings_Olinorder'( X, T, U ) ) ] )
% 1.18/1.62 , clause( 1192, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( T, Z
% 1.18/1.62 ), Y ) ), ~( 'c_Orderings_Olinorder'( T, X, U ) ) ] )
% 1.18/1.62 , clause( 1193, [ hBOOL( hAPP( hAPP( X, Y ), Y ) ), ~(
% 1.18/1.62 'c_Orderings_Olinorder'( Z, X, T ) ), hBOOL( hAPP( hAPP( Z, Y ), Y ) ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 1194, [ ~( hBOOL( hAPP( hAPP( X, Y ), Y ) ) ), ~(
% 1.18/1.62 'c_Orderings_Olinorder'( X, Z, T ) ), ~( hBOOL( hAPP( hAPP( Z, Y ), Y ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1195, [ =( 'c_Fun_Ofun__upd'( X, Y, hAPP( X, Y ), Z, T ), X ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 1196, [ =( hAPP( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), Y ), Z ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 1197, [ =( 'c_Fun_Ofun__upd'( X, Y, hAPP( X, Y ), Z, T ), X ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 1198, [ =( hAPP( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), Y ), Z ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 1199, [ =( 'c_Fun_Ofun__upd'( X, Y, hAPP( X, Y ), Z, T ), X ) ]
% 1.18/1.62 )
% 1.18/1.62 , clause( 1200, [ 'c_OrderedGroup_Oab__semigroup__idem__mult'( X, Y ), ~(
% 1.18/1.62 'c_Lattices_Olower__semilattice'( Z, T, X, Y ) ) ] )
% 1.18/1.62 , clause( 1201, [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.18/1.62 'c_Lattices_Olower__semilattice'( W, X, Y, V0 ) ) ] )
% 1.18/1.62 , clause( 1202, [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.18/1.62 'c_Lattices_Olower__semilattice'( W, X, Y, V0 ) ) ] )
% 1.18/1.62 , clause( 1203, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X
% 1.18/1.62 , Y ), hAPP( hAPP( T, U ), Z ) ) ) ), ~( 'c_Lattices_Olower__semilattice'(
% 1.18/1.62 X, W, T, V0 ) ) ] )
% 1.18/1.62 , clause( 1204, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X
% 1.18/1.62 , Y ), hAPP( hAPP( T, Z ), U ) ) ) ), ~( 'c_Lattices_Olower__semilattice'(
% 1.18/1.62 X, W, T, V0 ) ) ] )
% 1.18/1.62 , clause( 1205, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X
% 1.18/1.62 , Y ), hAPP( hAPP( T, Z ), U ) ) ) ), ~( 'c_Lattices_Olower__semilattice'(
% 1.18/1.62 X, W, T, V0 ) ) ] )
% 1.18/1.62 , clause( 1206, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X
% 1.18/1.62 , Y ), hAPP( hAPP( T, U ), Z ) ) ) ), ~( 'c_Lattices_Olower__semilattice'(
% 1.18/1.62 X, W, T, V0 ) ) ] )
% 1.18/1.62 , clause( 1207, [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.18/1.62 'c_Lattices_Olower__semilattice'( X, W, Y, V0 ) ) ] )
% 1.18/1.62 , clause( 1208, [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.18/1.62 'c_Lattices_Olower__semilattice'( X, W, Y, V0 ) ) ] )
% 1.18/1.62 , clause( 1209, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.18/1.62 'c_Lattices_Olower__semilattice'( 'c_COMBC'( 'c_lessequals'( X ), X, X,
% 1.18/1.62 'tc_bool' ), 'c_COMBC'( 'c_HOL_Oord__class_Oless'( X ), X, X, 'tc_bool' )
% 1.18/1.62 , 'c_Orderings_Oord__class_Omax'( X ), X ) ] )
% 1.18/1.62 , clause( 1210, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 1.18/1.62 , =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ] )
% 1.18/1.62 , clause( 1211, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), U ) ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1212, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.62 ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z )
% 1.18/1.62 , U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1213, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.62 X, 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , T ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1214, [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), Y ) ) ] )
% 1.18/1.62 , clause( 1215, [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), Z ) ) ] )
% 1.18/1.62 , clause( 1216, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1217, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1218, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1219, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), Z ) ) ] )
% 1.18/1.62 , clause( 1220, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), Y ) ) ] )
% 1.18/1.62 , clause( 1221, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.62 X, 'tc_bool' ) ), Y ), Z ) ), Y ) ) ] )
% 1.18/1.62 , clause( 1222, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.62 X, 'tc_bool' ) ), Y ), Z ) ), Z ) ) ] )
% 1.18/1.62 , clause( 1223, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1224, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1225, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.62 ), Y ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 1226, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 1227, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.62 ), Y ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.18/1.62 Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 1228, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.62 Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 1229, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1230, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1231, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1232, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1233, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1234, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.62 X, 'tc_bool' ) ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1235, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1236, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1237, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ) ] )
% 1.18/1.62 , clause( 1238, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ) ] )
% 1.18/1.62 , clause( 1239, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.62 X, 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), Z ) ) ] )
% 1.18/1.62 , clause( 1240, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 1241, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ) ) ] )
% 1.18/1.62 , clause( 1242, [ ~(
% 1.18/1.62 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.18/1.62 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1243, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), Y ) ] )
% 1.18/1.62 , clause( 1244, [ ~( hBOOL( hAPP( hAPP( X, Y ), Y ) ) ), ~(
% 1.18/1.62 'c_Orderings_Olinorder'( Z, X, T ) ) ] )
% 1.18/1.62 , clause( 1245, [ ~( 'c_Orderings_Olinorder'( X, Y, Z ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( Y, T ), T ) ) ) ] )
% 1.18/1.62 , clause( 1246, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OlessThan'( Y, X ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1247, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OlessThan'( Y, X )
% 1.18/1.62 ), 'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ) ) ] )
% 1.18/1.62 , clause( 1248, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.62 , T ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) )
% 1.18/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 1249, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1250, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.62 , T ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) )
% 1.18/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ] )
% 1.18/1.62 , clause( 1251, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1252, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.62 T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ] )
% 1.18/1.62 , clause( 1253, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.62 ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.62 T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ] )
% 1.18/1.62 , clause( 1254, [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), T )
% 1.18/1.62 ) ), ~( 'c_Lattices_Olower__semilattice'( X, W, Z, V0 ) ) ] )
% 1.18/1.62 , clause( 1255, [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ),
% 1.18/1.62 ~( 'c_Lattices_Olower__semilattice'( X, U, Y, W ) ) ] )
% 1.18/1.62 , clause( 1256, [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ),
% 1.18/1.62 ~( 'c_Lattices_Olower__semilattice'( X, U, Y, W ) ) ] )
% 1.18/1.62 , clause( 1257, [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), T )
% 1.18/1.62 ) ), ~( 'c_Lattices_Olower__semilattice'( X, W, Z, V0 ) ) ] )
% 1.18/1.62 , clause( 1258, [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), T )
% 1.18/1.62 ) ), ~( 'c_Lattices_Olower__semilattice'( X, W, Z, V0 ) ) ] )
% 1.18/1.62 , clause( 1259, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), Z ), Y ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1260, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), Z ), Z ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Z ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1261, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Y ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1262, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 1.18/1.62 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ),
% 1.18/1.62 Y ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ] )
% 1.18/1.62 , clause( 1263, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Z ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1264, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.62 X, 'tc_bool' ) ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1265, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Z ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1266, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1267, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.18/1.62 X, 'tc_bool' ) ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1268, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1269, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1270, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1271, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1272, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1273, [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1274, [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1275, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1276, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1277, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1278, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1279, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1280, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), T ), Y ) ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1281, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 1282, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 1283, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 1284, [ 'c_Complete__Lattice_Ocomplete__lattice'( X, Y, 'c_COMBC'(
% 1.18/1.62 Z, T, T, 'tc_bool' ), 'c_COMBC'( U, T, T, 'tc_bool' ), W, V0, V1, V2, T )
% 1.18/1.62 , ~( 'c_Complete__Lattice_Ocomplete__lattice'( Y, X, Z, U, V0, W, V2, V1
% 1.18/1.62 , T ) ) ] )
% 1.18/1.62 , clause( 1285, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 1286, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.18/1.62 'c_SetInterval_Oord__class_OlessThan'( Y, X ),
% 1.18/1.62 'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ), =( Y, Z ) ] )
% 1.18/1.62 , clause( 1287, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), T ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U ) ) ] )
% 1.18/1.62 , clause( 1288, [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ), hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ) ] )
% 1.18/1.62 , clause( 1289, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ), Y
% 1.18/1.62 ) ) ] )
% 1.18/1.62 , clause( 1290, [ =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Z ), T ) ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), T ), Y ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Z ), T ) ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.62 'tc_fun'( X, 'tc_bool' ) ), T ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1291, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.18/1.62 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1292, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.18/1.62 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.18/1.62 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 1.18/1.62 , clause( 1293, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.62 ) ), =( Y, Z ) ] )
% 1.18/1.62 , clause( 1294, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.18/1.62 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.62 ) ), =( Y, Z ) ] )
% 1.18/1.62 , clause( 1295, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 1296, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 1297, [ =( 'c_Fun_Ofun__upd'( 'c_Map_Orestrict__map'( X, Y, Z, T
% 1.18/1.62 ), U, 'c_Option_Ooption_ONone'( T ), Z, 'tc_Option_Ooption'( T ) ),
% 1.18/1.62 'c_Map_Orestrict__map'( X, Y, Z, T ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), U
% 1.18/1.62 ), Y ) ) ] )
% 1.18/1.62 , clause( 1298, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1299, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1300, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ) ) ] )
% 1.18/1.62 , clause( 1301, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), T ), Z ) ) ) ) ] )
% 1.18/1.62 , clause( 1302, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1303, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1304, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( T, U, X ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Y ), T ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Z ), U ), X ) ) ] )
% 1.18/1.62 , clause( 1305, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.18/1.62 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1306, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.18/1.62 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1307, [ =( 'c_Finite__Set_Ofold'( X, Y, Z, T, U ), W ), ~( hBOOL(
% 1.18/1.62 hAPP( 'c_Finite__Set_Ofold__graph'( X, Y, Z, T, U ), W ) ) ), ~(
% 1.18/1.62 'c_Finite__Set_Ofun__left__comm'( X, T, U ) ) ] )
% 1.18/1.62 , clause( 1308, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1309, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 1310, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.18/1.62 X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1311, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.18/1.62 X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 1312, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.18/1.62 X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1313, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.18/1.62 X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.62 , clause( 1314, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.18/1.62 X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1315, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ) ) ] )
% 1.18/1.62 , clause( 1316, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.62 , 'c_Suc'( X ) ), Y ) ), =( 'c_Suc'( X ), Y ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1317, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.18/1.62 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 1.18/1.62 , clause( 1318, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 1.18/1.62 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 1.18/1.62 , clause( 1319, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 1.18/1.62 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 1.18/1.62 , clause( 1320, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 1.18/1.62 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ] )
% 1.18/1.62 , clause( 1321, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), 'c_Set_Ovimage'( Y, Z, X, T ) ), 'c_Set_Ovimage'( Y, U, X, T ) ) )
% 1.18/1.62 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( T, 'tc_bool' ) ), Z ),
% 1.18/1.62 U ) ) ) ] )
% 1.18/1.62 , clause( 1322, [ ~(
% 1.18/1.62 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 1.18/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1323, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.18/1.62 'c_Lattices_Olower__semilattice'( 'c_COMBC'( 'c_lessequals'( X ), X, X,
% 1.18/1.62 'tc_bool' ), 'c_COMBC'( 'c_HOL_Oord__class_Oless'( X ), X, X, 'tc_bool' )
% 1.18/1.62 , 'c_Lattices_Oupper__semilattice__class_Osup'( X ), X ) ] )
% 1.18/1.62 , clause( 1324, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , T ), Z ) ) ) ) ] )
% 1.18/1.62 , clause( 1325, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.62 ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.62 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.62 , Z ), T ) ) ) ) ] )
% 1.18/1.62 , clause( 1326, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ) ] )
% 1.18/1.62 , clause( 1327, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), T ), Z ) ) ) ) ] )
% 1.18/1.62 , clause( 1328, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1329, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ) ), ~(
% 1.18/1.62 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1330, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ) ] )
% 1.18/1.62 , clause( 1331, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), T ), Z ) ) ) ) ] )
% 1.18/1.62 , clause( 1332, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), 'c_Finite__Set_Ofold'(
% 1.18/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y, Z, X, X ) ), hAPP(
% 1.18/1.62 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), T ), Y ) ) ),
% 1.18/1.62 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Z ) ) ), ~(
% 1.18/1.62 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.18/1.62 , clause( 1333, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Y,
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 1334, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP(
% 1.18/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Z,
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 1335, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.62 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) )
% 1.18/1.62 ) ] )
% 1.18/1.62 , clause( 1336, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 1.18/1.62 ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), ~( =( hAPP( Y, Z )
% 1.18/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T )
% 1.18/1.62 , Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ), =(
% 1.18/1.62 'c_Finite__Set_Osetprod'( Y, U, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.62 ] )
% 1.18/1.62 , clause( 1337, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.62 ~( =( hAPP( Y, Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.62 hAPP( 'c_in'( T ), Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ),
% 1.18/1.62 =( 'c_Finite__Set_Osetprod'( Y, U, T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.62 ) ) ] )
% 1.18/1.62 , clause( 1338, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Z ), Y ) ) ] )
% 1.18/1.62 , clause( 1339, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( X ), T ), U ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), U ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( U, Y, X ) ),
% 1.18/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( T, Z, X ) ) ) ) ] )
% 1.18/1.62 , clause( 1340, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ),
% 1.18/1.62 hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), T ) ) ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ) ) ] )
% 1.18/1.62 , clause( 1341, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omax'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), Y ) ] )
% 1.18/1.62 , clause( 1342, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.18/1.62 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), T ), Y ) ) ) ] )
% 1.18/1.62 , clause( 1343, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.62 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), T ), Z ) ) ) ] )
% 1.18/1.62 , clause( 1344, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.18/1.62 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.62 , clause( 1345, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.62 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1346, [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), hBOOL(
% 1.18/1.62 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.62 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.62 'c_lessequals'( X ), Z ), T ) ) ) ] )
% 1.18/1.62 , clause( 1347, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.18/1.62 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.18/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 1348, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 1349, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.62 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.62 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.18/1.62 , clause( 1350, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 1.18/1.62 , clause( 1351, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 1.18/1.62 , clause( 1352, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.18/1.63 =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ),
% 1.18/1.63 'c_Complete__Lattice_OSup__class_OSup'( Z, X ) ), 'c_Finite__Set_Ofold'(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y, Z, X, X ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.18/1.63 , clause( 1353, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP(
% 1.18/1.63 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Y ), Y ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1354, [ =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), Y ), Y ) ] )
% 1.18/1.63 , clause( 1355, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), T ), Y ) ), Z ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1356, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ), Z ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1357, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1358, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1359, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), T ), Y ) ), Z ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1360, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ), Z ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1361, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1362, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ), T ), Y ) ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1363, [ ~(
% 1.18/1.63 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1364, [ ~(
% 1.18/1.63 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1365, [ ~(
% 1.18/1.63 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ] )
% 1.18/1.63 , clause( 1366, [ ~(
% 1.18/1.63 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ] )
% 1.18/1.63 , clause( 1367, [ ~(
% 1.18/1.63 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ] )
% 1.18/1.63 , clause( 1368, [ ~(
% 1.18/1.63 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ] )
% 1.18/1.63 , clause( 1369, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( 't_a', X ) ), Y )
% 1.18/1.63 , Z ), 'v_x' ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.18/1.63 X ), hAPP( Y, 'v_x' ) ), hAPP( Z, 'v_x' ) ) ) ] )
% 1.18/1.63 , clause( 1370, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.63 ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Z ) ) )
% 1.18/1.63 ] )
% 1.18/1.63 , clause( 1371, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1372, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), T ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1373, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.18/1.63 ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.63 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.63 , clause( 1374, [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.63 ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) )
% 1.18/1.63 ] )
% 1.18/1.63 , clause( 1375, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), Y ), Y ) ) ] )
% 1.18/1.63 , clause( 1376, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), Y ), Y ) ) ] )
% 1.18/1.63 , clause( 1377, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1378, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( Z, Y ) ) ), ~(
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( T, 'tc_bool' ) ), Z ), X ) )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1379, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), Y ) ) ] )
% 1.18/1.63 , clause( 1380, [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), Y ) ) ] )
% 1.18/1.63 , clause( 1381, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( Z, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.63 'tc_fun'( Y, 'tc_bool' ) ), X ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1382, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X
% 1.18/1.63 , 'tc_bool' ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1383, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X
% 1.18/1.63 , 'tc_bool' ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), T ), Z ) ) ), ~(
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1384, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( 'tc_fun'( Z, 'tc_bool' ) ), T ), X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.63 T, Y ) ) ) ] )
% 1.18/1.63 , clause( 1385, [ 'c_Finite__Set_Ofinite'( X, Y ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( 'tc_fun'( Y, 'tc_bool' ) ), X ), Z ) ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( Z, Y ) ) ] )
% 1.18/1.63 , clause( 1386, [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1387, [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1388, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), U ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.63 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1389, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.63 'c_SetInterval_Oord__class_OatLeastAtMost'( T, U, X ) ),
% 1.18/1.63 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ) ) ) ] )
% 1.18/1.63 , clause( 1390, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.18/1.63 'c_OrderedGroup_Oab__semigroup__idem__mult'(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( X ), X ) ] )
% 1.18/1.63 , clause( 1391, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.18/1.63 X, 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , T ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1392, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) )
% 1.18/1.63 ] )
% 1.18/1.63 , clause( 1393, [ =( hAPP( 'c_Fun_Ofun__upd'( X, Y, hAPP(
% 1.18/1.63 'c_Option_Ooption_OSome'( Z ), T ), U, 'tc_Option_Ooption'( Z ) ), Y ),
% 1.18/1.63 hAPP( 'c_Option_Ooption_OSome'( Z ), T ) ) ] )
% 1.18/1.63 , clause( 1394, [ ~( =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ),
% 1.18/1.63 T ) ) ), =( 'c_Fun_Ofun__upd'( X, Y, hAPP( 'c_Option_Ooption_OSome'( Z )
% 1.18/1.63 , T ), U, 'tc_Option_Ooption'( Z ) ), X ) ] )
% 1.18/1.63 , clause( 1395, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 1.18/1.63 , =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ] )
% 1.18/1.63 , clause( 1396, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.63 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ),
% 1.18/1.63 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1397, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.63 , X ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.63 , 'c_Suc'( X ) ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1398, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.63 , X ), 'c_Suc'( Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.63 'tc_nat' ), X ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1399, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1400, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.63 X ), Z ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.18/1.63 ) ) ) ] )
% 1.18/1.63 , clause( 1401, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.63 ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ] )
% 1.18/1.63 , clause( 1402, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.63 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.63 ) ) ) ] )
% 1.18/1.63 , clause( 1403, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.63 ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ] )
% 1.18/1.63 , clause( 1404, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =(
% 1.18/1.63 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y,
% 1.18/1.63 'tc_bool' ) ), Z ), T ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.18/1.63 'tc_bool' ) ) ) ), ~( 'c_Finite__Set_Ofinite'( T, Y ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( Z, Y ) ), =( 'c_Finite__Set_Ofold__image'(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), U, 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.18/1.63 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y,
% 1.18/1.63 'tc_bool' ) ), Z ), T ), X, Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.63 X ), 'c_Finite__Set_Ofold__image'( 'c_HOL_Oplus__class_Oplus'( X ), U,
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ), Z, X, Y ) ),
% 1.18/1.63 'c_Finite__Set_Ofold__image'( 'c_HOL_Oplus__class_Oplus'( X ), U,
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ), T, X, Y ) ) ) ] )
% 1.18/1.63 , clause( 1405, [ =( X, Y ), hBOOL( hAPP( hAPP( Z, Y ), X ) ), hBOOL( hAPP(
% 1.18/1.63 hAPP( Z, X ), Y ) ), ~( 'c_Orderings_Olinorder'( T, Z, U ) ) ] )
% 1.18/1.63 , clause( 1406, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Z
% 1.18/1.63 ), Y ) ), =( Z, Y ), ~( 'c_Orderings_Olinorder'( T, X, U ) ) ] )
% 1.18/1.63 , clause( 1407, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.18/1.63 hAPP( X, Z ), Y ) ), ~( 'c_Orderings_Olinorder'( T, X, U ) ) ] )
% 1.18/1.63 , clause( 1408, [ =( X, Y ), hBOOL( hAPP( hAPP( Z, X ), Y ) ), hBOOL( hAPP(
% 1.18/1.63 hAPP( Z, Y ), X ) ), ~( 'c_Orderings_Olinorder'( T, Z, U ) ) ] )
% 1.18/1.63 , clause( 1409, [ hBOOL( hAPP( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), Z ), T ) ), ~( hBOOL( hAPP( Z, T ) ) ), ~( hBOOL( hAPP( Y, T ) ) )
% 1.18/1.63 ] )
% 1.18/1.63 , clause( 1410, [ =( hAPP( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), W ), hAPP( X
% 1.18/1.63 , W ) ), =( W, Y ) ] )
% 1.18/1.63 , clause( 1411, [ =( hAPP( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), W ), hAPP( X
% 1.18/1.63 , W ) ), =( W, Y ) ] )
% 1.18/1.63 , clause( 1412, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y )
% 1.18/1.63 , hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ), hAPP(
% 1.18/1.63 hAPP( 'c_Orderings_Oord__class_Omin'( X ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ) ) ) ] )
% 1.18/1.63 , clause( 1413, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.63 'c_Orderings_Oord__class_Omin'( X ), X ), Y ) ), hAPP(
% 1.18/1.63 'c_Finite__Set_Ofold1'( 'c_Orderings_Oord__class_Omin'( X ), X ), Z ) ) )
% 1.18/1.63 , ~( 'c_Finite__Set_Ofinite'( Y, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Z ), Y ) ) ), =( Z,
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.18/1.63 , clause( 1414, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.18/1.63 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 1.18/1.63 T, 'tc_bool' ) ), Z ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( T
% 1.18/1.63 , 'tc_bool' ) ), X ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.63 'tc_fun'( T, 'tc_bool' ) ), Z ), X ) ) ) ] )
% 1.18/1.63 , clause( 1415, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.18/1.63 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.18/1.63 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), U ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.63 ), Z ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1416, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.18/1.63 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.18/1.63 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.63 ), U ), T ) ) ) ] )
% 1.18/1.63 , clause( 1417, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.18/1.63 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.18/1.63 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), T ), U ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1418, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.18/1.63 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.18/1.63 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), T ), U ) ) ) ] )
% 1.18/1.63 , clause( 1419, [ ~( 'class_Orderings_Oorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , 'c_SetInterval_Oord__class_OlessThan'( Y, X ) ),
% 1.18/1.63 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.18/1.63 , clause( 1420, [ 'c_Finite__Set_Ofun__left__comm'( X, Y, Y ), ~(
% 1.18/1.63 'c_OrderedGroup_Oab__semigroup__mult'( X, Y ) ) ] )
% 1.18/1.63 , clause( 1421, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omin'( X ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ) ] )
% 1.18/1.63 , clause( 1422, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omin'( X ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1423, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1424, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), Z ) ) ), =( Z, Y ) ] )
% 1.18/1.63 , clause( 1425, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X
% 1.18/1.63 , 'tc_bool' ) ), Y ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1426, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1427, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1428, [ =( X, Y ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.63 'tc_fun'( Z, 'tc_bool' ) ), X ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( 'tc_fun'( Z, 'tc_bool' ) ), X ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1429, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1430, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), Z ) ) ), =( Y, Z ) ] )
% 1.18/1.63 , clause( 1431, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ] )
% 1.18/1.63 , clause( 1432, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1433, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.18/1.63 X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.63 X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~(
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.63 , Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1434, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.63 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.63 , clause( 1435, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.63 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.63 X ) ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1436, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.63 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1437, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.18/1.63 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.63 , clause( 1438, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.18/1.63 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.18/1.63 , clause( 1439, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ),
% 1.18/1.63 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.63 ) ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1440, [ ~( =( 'c_Fun_Ofun__upd'( X, Y, hAPP(
% 1.18/1.63 'c_Option_Ooption_OSome'( Z ), T ), U, 'tc_Option_Ooption'( Z ) ),
% 1.18/1.63 'c_Fun_Ofun__upd'( W, Y, hAPP( 'c_Option_Ooption_OSome'( Z ), V0 ), U,
% 1.18/1.63 'tc_Option_Ooption'( Z ) ) ) ), =( T, V0 ) ] )
% 1.18/1.63 , clause( 1441, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.63 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ),
% 1.18/1.63 'c_SetInterval_Oord__class_OatLeastAtMost'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), Z ) ) ] )
% 1.18/1.63 , clause( 1442, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.63 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ] )
% 1.18/1.63 , clause( 1443, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ] )
% 1.18/1.63 , clause( 1444, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.63 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ] )
% 1.18/1.63 , clause( 1445, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ] )
% 1.18/1.63 , clause( 1446, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.63 , X ), X ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X
% 1.18/1.63 ), 'c_Suc'( X ) ) ) ] )
% 1.18/1.63 , clause( 1447, [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.18/1.63 ), X ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.63 'tc_nat' ), Y ), 'c_Suc'( X ) ) ) ) ] )
% 1.18/1.63 , clause( 1448, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.63 , X ), 'c_Suc'( Y ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.63 'tc_nat' ), Y ), X ) ) ] )
% 1.18/1.63 , clause( 1449, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1450, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1451, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1452, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1453, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1454, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.63 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1455, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1456, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1457, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1458, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.18/1.63 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1459, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1460, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1461, [ ~(
% 1.18/1.63 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1462, [ ~(
% 1.18/1.63 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.18/1.63 , clause( 1463, [ =( X, Y ), hBOOL( hAPP( hAPP( Z, X ), Y ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( T, X ), Y ) ) ), ~( 'c_Orderings_Olinorder'( T, Z, U ) ) ] )
% 1.18/1.63 , clause( 1464, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, X ), Y ) ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( T, X ), Y ) ), ~( 'c_Orderings_Olinorder'( Z, T, U ) ) ] )
% 1.18/1.63 , clause( 1465, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.18/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1466, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.18/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1467, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ) ] )
% 1.18/1.63 , clause( 1468, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Z ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1469, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.18/1.63 , T ), X ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1470, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.18/1.63 , X ), T ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1471, [ ~( =( 'c_Fun_Ofun__upd'( X, Y, Z, T, U ), X ) ), =( hAPP(
% 1.18/1.63 X, Y ), Z ) ] )
% 1.18/1.63 , clause( 1472, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.63 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.63 X ), Y ), T ) ), Z ) ) ] )
% 1.18/1.63 , clause( 1473, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.63 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y ) ] )
% 1.18/1.63 , clause( 1474, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.63 X ) ), Y ), Y ) ] )
% 1.18/1.63 , clause( 1475, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.18/1.63 'class_Int_Onumber__ring'( X ) ), =( Y, hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.63 ] )
% 1.18/1.63 , clause( 1476, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 1.18/1.63 , clause( 1477, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.63 , Y ), Y ) ] )
% 1.18/1.63 , clause( 1478, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.63 ) ), Y ) ] )
% 1.18/1.63 , clause( 1479, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.63 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 1.18/1.63 , clause( 1480, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.63 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y ) ] )
% 1.18/1.63 , clause( 1481, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.63 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.63 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ) ) ] )
% 1.18/1.63 , clause( 1482, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ) ] )
% 1.18/1.63 , clause( 1483, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.63 X ) ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ] )
% 1.18/1.63 , clause( 1484, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.63 X ) ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ] )
% 1.18/1.63 , clause( 1485, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.63 X ) ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ] )
% 1.18/1.63 , clause( 1486, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.63 X ) ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ] )
% 1.18/1.63 , clause( 1487, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.18/1.63 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.63 , Y ), Z ), Z, X ), Y ) ] )
% 1.18/1.63 , clause( 1488, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.63 ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.18/1.63 , T, X ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, U, X ) ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1489, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.63 ), T ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( T
% 1.18/1.63 , Y, X ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( U, Z, X ) ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1490, [ hBOOL( hAPP( hAPP( X, 'c_Finite__Set_Ofold'( Y, Z, T, U,
% 1.18/1.63 U ) ), hAPP( hAPP( Y, W ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W
% 1.18/1.63 ), T ) ) ), ~( 'c_Finite__Set_Ofinite'( T, U ) ), ~(
% 1.18/1.63 'c_Lattices_Olower__semilattice'( X, V0, Y, U ) ) ] )
% 1.18/1.63 , clause( 1491, [ =( hAPP( hAPP( X, Y ), 'c_Finite__Set_Ofold'( X, Z, T, U
% 1.18/1.63 , W ) ), 'c_Finite__Set_Ofold'( X, hAPP( hAPP( X, Y ), Z ), T, U, W ) ),
% 1.18/1.63 ~( 'c_Finite__Set_Ofinite'( T, U ) ), ~( 'c_Finite__Set_Ofun__left__comm'(
% 1.18/1.63 X, U, W ) ) ] )
% 1.18/1.63 , clause( 1492, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1493, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1494, [ ~(
% 1.18/1.63 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1495, [ ~(
% 1.18/1.63 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1496, [ =( 'c_Set_Ovimage'( X, hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.63 , Z ), T ), U, Y ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( U, 'tc_bool' ) )
% 1.18/1.63 , 'c_Set_Ovimage'( X, Z, U, Y ) ), 'c_Set_Ovimage'( X, T, U, Y ) ) ) ] )
% 1.18/1.63 , clause( 1497, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.63 , 'c_Suc'( X ) ), 'c_Suc'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1498, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.63 , X ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.63 , 'c_Suc'( X ) ), 'c_Suc'( Y ) ) ) ) ] )
% 1.18/1.63 , clause( 1499, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.18/1.63 , 'c_Suc'( X ) ), 'c_Suc'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1500, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ] )
% 1.18/1.63 , clause( 1501, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.63 X ), Y ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1502, [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.18/1.63 , clause( 1503, [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.18/1.63 , clause( 1504, [ ~( 'class_HOL_Oord'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), hAPP( Y, Z ) ), hAPP( T, Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( 'tc_fun'( U, X ) ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1505, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1506, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1507, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), T ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1508, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), T ), Z ) ) ), ~(
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1509, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), T ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1510, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), T ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1511, [ =( hAPP( 'c_Map_Orestrict__map'( X, Y, Z, T ), U ), hAPP(
% 1.18/1.63 X, U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1512, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), T ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1513, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , T ), Z ) ) ) ) ] )
% 1.18/1.63 , clause( 1514, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Z ), T ) ) ) ) ] )
% 1.18/1.63 , clause( 1515, [ ~( =( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ), 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'(
% 1.18/1.63 X, 'tc_bool' ), 'tc_bool' ), Z ) ) ), =( Y, Z ) ] )
% 1.18/1.63 , clause( 1516, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ),
% 1.18/1.63 hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.63 X ), Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ), X, X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_in'( X ), Z ), T ) ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z, T, X, X ), U ) ) ) ] )
% 1.18/1.63 , clause( 1517, [ ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y, Z, T
% 1.18/1.63 , U ), W ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), V0 ), Z ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofun__left__comm'( X, T, U ) ), hBOOL( hAPP(
% 1.18/1.63 'c_Finite__Set_Ofold__graph'( X, Y, hAPP( hAPP( 'c_Set_Oinsert'( T ), V0
% 1.18/1.63 ), Z ), T, U ), hAPP( hAPP( X, V0 ), W ) ) ) ] )
% 1.18/1.63 , clause( 1518, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X
% 1.18/1.63 , 'tc_bool' ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~(
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) )
% 1.18/1.63 ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1519, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X
% 1.18/1.63 , 'tc_bool' ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~(
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) )
% 1.18/1.63 ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.18/1.63 X ), Z ), T ) ) ] )
% 1.18/1.63 , clause( 1520, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Y ) ), hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_in'( X ), T ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( X ), T ), Z ) ) ) ) ] )
% 1.18/1.63 , clause( 1521, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL(
% 1.18/1.63 hAPP( 'c_Finite__Set_Ofold__graph'( 'c_HOL_Oplus__class_Oplus'( X ), Y,
% 1.18/1.63 hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ), X, X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), U ) ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.18/1.63 X ), Z ), T ) ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ), U ) ) ) ] )
% 1.18/1.63 , clause( 1522, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP(
% 1.18/1.63 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( X ) ), Y ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.18/1.63 , clause( 1523, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP(
% 1.18/1.63 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( X ) ), 'c_Orderings_Obot__class_Obot'( X
% 1.18/1.63 ) ) ] )
% 1.18/1.63 , clause( 1524, [ ~( 'class_Orderings_Obot'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), 'c_Orderings_Obot__class_Obot'( X ) ), Y ) ) ] )
% 1.18/1.63 , clause( 1525, [ =( 'c_Finite__Set_Ofold__image'( X, Y, Z,
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), U, T ), Z ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1526, [ =( 'c_Finite__Set_Ofold'( X, Y,
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), Y ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1527, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ] )
% 1.18/1.63 , clause( 1528, [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.18/1.63 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( Y,
% 1.18/1.63 'tc_bool' ) ), X ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.18/1.63 'tc_bool' ) ) ) ) ) ] )
% 1.18/1.63 , clause( 1529, [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'(
% 1.18/1.63 X, 'tc_bool' ) ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ) ) ) ) ] )
% 1.18/1.63 , clause( 1530, [ =( X, Y ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'(
% 1.18/1.63 Z, Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T, U )
% 1.18/1.63 , X ) ) ) ] )
% 1.18/1.63 , clause( 1531, [ =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.18/1.63 , clause( 1532, [ =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), Y ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.18/1.63 , clause( 1533, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), Y ) )
% 1.18/1.63 ] )
% 1.18/1.63 , clause( 1534, [ hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y,
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), Y ) )
% 1.18/1.63 ] )
% 1.18/1.63 , clause( 1535, [ 'c_Nitpick_Ofold__graph_H'( X, Y,
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Y, Z, T ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1536, [ =( hAPP( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( 't_a', 'tc_bool'
% 1.18/1.63 ) ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool'
% 1.18/1.63 ), 'tc_bool' ), X ) ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'(
% 1.18/1.63 't_a', 'tc_bool' ), 'tc_bool' ), Y ) ), 'v_x' ), hAPP( hAPP( 'c_in'(
% 1.18/1.63 't_a' ), 'v_x' ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( 't_a', 'tc_bool'
% 1.18/1.63 ) ), X ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1537, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ), Z ), T ) ) ) ] )
% 1.18/1.63 , clause( 1538, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1539, [ =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( X ), Y ), T ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.18/1.63 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ), Z ), T ) ) ) ] )
% 1.18/1.63 , clause( 1540, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1541, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), Y ) ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1542, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.18/1.63 'c_Complete__Lattice_OSup__class_OSup'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1543, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ] )
% 1.18/1.63 , clause( 1544, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.63 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ] )
% 1.18/1.63 , clause( 1545, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.63 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ] )
% 1.18/1.63 , clause( 1546, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.63 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ] )
% 1.18/1.63 , clause( 1547, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.63 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1548, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.63 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ] )
% 1.18/1.63 , clause( 1549, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.63 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.63 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 1.18/1.63 ) ) ] )
% 1.18/1.63 , clause( 1550, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.63 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 1.18/1.63 ) ) ] )
% 1.18/1.63 , clause( 1551, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.18/1.63 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.63 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.63 ) ) ] )
% 1.18/1.63 , clause( 1552, [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1553, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1554, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.63 Z ), Y ) ) ] )
% 1.18/1.63 , clause( 1555, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1556, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1557, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.63 'c_Finite__Set_Ofold__image'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, hAPP(
% 1.18/1.63 hAPP( 'c_Set_Oinsert'( T ), U ), W ), X, T ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, U ) ),
% 1.18/1.63 'c_Finite__Set_Ofold__image'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, W, X
% 1.18/1.63 , T ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), U ), W ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( W, T ) ) ] )
% 1.18/1.63 , clause( 1558, [ =( 'c_Finite__Set_Ofold'( X, Y, hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( Z ), T ), U ), Z, W ), 'c_Finite__Set_Ofold'( X, hAPP(
% 1.18/1.63 hAPP( X, T ), Y ), U, Z, W ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U )
% 1.18/1.63 ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofun__left__comm'( X, Z, W ) ) ] )
% 1.18/1.63 , clause( 1559, [ =( 'c_Finite__Set_Ofold'( X, Y, hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( Z ), T ), U ), Z, W ), hAPP( hAPP( X, T ),
% 1.18/1.63 'c_Finite__Set_Ofold'( X, Y, U, Z, W ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z
% 1.18/1.63 ), T ), U ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofun__left__comm'( X, Z, W ) ) ] )
% 1.18/1.63 , clause( 1560, [ =( 'c_Finite__Set_Ocard'( hAPP( hAPP( 'c_Set_Oinsert'( X
% 1.18/1.63 ), Y ), Z ), X ), 'c_Suc'( 'c_Finite__Set_Ocard'( Z, X ) ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) )
% 1.18/1.63 ] )
% 1.18/1.63 , clause( 1561, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.63 'c_Finite__Set_Osetsum'( Y, hAPP( hAPP( 'c_Set_Oinsert'( Z ), T ), U ), Z
% 1.18/1.63 , X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, T ) ),
% 1.18/1.63 'c_Finite__Set_Osetsum'( Y, U, Z, X ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.18/1.63 , T ), U ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ) ] )
% 1.18/1.63 , clause( 1562, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.18/1.63 'c_Finite__Set_Ofold__image'( 'c_HOL_Otimes__class_Otimes'( X ), Y, Z,
% 1.18/1.63 hAPP( hAPP( 'c_Set_Oinsert'( T ), U ), W ), X, T ), hAPP( hAPP(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, U ) ),
% 1.18/1.63 'c_Finite__Set_Ofold__image'( 'c_HOL_Otimes__class_Otimes'( X ), Y, Z, W
% 1.18/1.63 , X, T ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), U ), W ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( W, T ) ) ] )
% 1.18/1.63 , clause( 1563, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.18/1.63 'c_Finite__Set_Osetprod'( Y, hAPP( hAPP( 'c_Set_Oinsert'( Z ), T ), U ),
% 1.18/1.63 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, T ) ),
% 1.18/1.63 'c_Finite__Set_Osetprod'( Y, U, Z, X ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z
% 1.18/1.63 ), T ), U ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ) ] )
% 1.18/1.63 , clause( 1564, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ),
% 1.18/1.63 'c_Finite__Set_Ofold'( 'c_Lattices_Oupper__semilattice__class_Osup'( X )
% 1.18/1.63 , Z, T, X, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( T, X ) ) ] )
% 1.18/1.63 , clause( 1565, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), =(
% 1.18/1.63 'c_Finite__Set_Ocard'( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), X ),
% 1.18/1.63 'c_Suc'( 'c_Finite__Set_Ocard'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.18/1.63 X, 'tc_bool' ) ), X ) ) ) ] )
% 1.18/1.63 , clause( 1566, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.18/1.63 =( 'c_Complete__Lattice_OSup__class_OSup'( Y, X ), 'c_Finite__Set_Ofold'(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( X ), Y, X, X ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.18/1.63 , clause( 1567, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.63 'c_Finite__Set_Osetsum'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'(
% 1.18/1.63 U, 'tc_bool' ) ), U, X ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.63 'c_Finite__Set_Osetsum'( Y, Z, U, X ), 'c_Finite__Set_Osetsum'( Y, T, U,
% 1.18/1.63 X ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( U, 'tc_bool'
% 1.18/1.63 ) ), T ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, U ) ) ] )
% 1.18/1.63 , clause( 1568, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X
% 1.18/1.63 , 'tc_bool' ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~(
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) )
% 1.18/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_bool' ) ) ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) )
% 1.18/1.63 ] )
% 1.18/1.63 , clause( 1569, [ =( 'c_Fun_Ofun__upd'( 'c_Map_Orestrict__map'( X, Y, Z, T
% 1.18/1.63 ), U, W, Z, 'tc_Option_Ooption'( T ) ), 'c_Fun_Ofun__upd'(
% 1.18/1.63 'c_Map_Orestrict__map'( X, 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( Z ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.18/1.63 'tc_bool' ) ) ), 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), U, W, Z,
% 1.18/1.63 'tc_Option_Ooption'( T ) ) ) ] )
% 1.18/1.63 , clause( 1570, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( X ), X ), Y ) ), Z ) ), ~(
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ), ~( 'c_Finite__Set_Ofinite'(
% 1.18/1.63 Y, X ) ) ] )
% 1.18/1.63 , clause( 1571, [ =( hAPP( 'c_Finite__Set_Ofold1'( X, Y ), hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( Y ), Z ), T ) ), 'c_Finite__Set_Ofold'( X, Z, T, Y, Y )
% 1.18/1.63 ), ~( 'c_Finite__Set_Ofinite'( T, Y ) ), ~(
% 1.18/1.63 'c_OrderedGroup_Oab__semigroup__idem__mult'( X, Y ) ) ] )
% 1.18/1.63 , clause( 1572, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 1.18/1.63 , =( hAPP( 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X )
% 1.18/1.63 , hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), 'c_Finite__Set_Ofold'(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y, Z, X, X ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.18/1.63 , clause( 1573, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.18/1.63 'c_Finite__Set_Olinorder__class_OMax'( X ), Y ), Z ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_in'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.63 ), 'c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1'(
% 1.18/1.63 Y, Z, X ) ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.18/1.63 , clause( 1574, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.18/1.63 'c_Finite__Set_Olinorder__class_OMin'( X ), Y ), Z ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_in'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.18/1.63 ), Z ),
% 1.18/1.63 'c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1'( Y,
% 1.18/1.63 Z, X ) ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.18/1.63 , clause( 1575, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), hAPP( 'c_Finite__Set_Olinorder__class_OMax'( X ), Y
% 1.18/1.63 ) ), hAPP( 'c_Finite__Set_Olinorder__class_OMax'( X ), Z ) ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1576, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), hAPP( 'c_Finite__Set_Olinorder__class_OMin'( X ), Y
% 1.18/1.63 ) ), hAPP( 'c_Finite__Set_Olinorder__class_OMin'( X ), Z ) ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( Y, X ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ), Z ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1577, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , T ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1578, [ hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y, hAPP(
% 1.18/1.63 hAPP( 'c_Set_Oinsert'( Z ), T ), U ), Z, W ), hAPP( hAPP( X, T ), V0 ) )
% 1.18/1.63 ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y, U, Z, W ), V0 ) )
% 1.18/1.63 ), hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ) ] )
% 1.18/1.63 , clause( 1579, [ =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Z ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ] )
% 1.18/1.63 , clause( 1580, [ =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ] )
% 1.18/1.63 , clause( 1581, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), Z ) ) ) ),
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Y ) ) ] )
% 1.18/1.63 , clause( 1582, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ] )
% 1.18/1.63 , clause( 1583, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Y ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( X ), T ), Z ) ) ) ) ] )
% 1.18/1.63 , clause( 1584, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ] )
% 1.18/1.63 , clause( 1585, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( X ), Y ), T ) ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1586, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X
% 1.18/1.63 , 'tc_bool' ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Z )
% 1.18/1.63 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), Z ) ) ) ) ] )
% 1.18/1.63 , clause( 1587, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X
% 1.18/1.63 , 'tc_bool' ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~(
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1588, [ =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1589, [ =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( X ), Z ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1590, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Z ), T ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1591, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.18/1.63 =( 'c_Complete__Lattice_OSup__class_OSup'( 'c_Orderings_Obot__class_Obot'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ), X ), 'c_Orderings_Obot__class_Obot'( X ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1592, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.18/1.63 =( 'c_Complete__Lattice_OSup__class_OSup'( hAPP( hAPP( 'c_Set_Oinsert'( X
% 1.18/1.63 ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), X
% 1.18/1.63 ), Y ) ] )
% 1.18/1.63 , clause( 1593, [ =( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ), =( X,
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( 'tc_fun'( Y, 'tc_bool' ) ), X ), hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.18/1.63 'tc_bool' ) ) ) ) ) ) ] )
% 1.18/1.63 , clause( 1594, [ =( 'c_Fun_Ofun__upd'( 'c_Map_Orestrict__map'( X, Y, Z, T
% 1.18/1.63 ), U, W, Z, 'tc_Option_Ooption'( T ) ), 'c_Fun_Ofun__upd'(
% 1.18/1.63 'c_Map_Orestrict__map'( X, 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( Z ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.18/1.63 'tc_bool' ) ) ), 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), U, W, Z,
% 1.18/1.63 'tc_Option_Ooption'( T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), Y )
% 1.18/1.63 ) ) ] )
% 1.18/1.63 , clause( 1595, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X
% 1.18/1.63 , 'tc_bool' ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~(
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) )
% 1.18/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_bool' ) ) ), T ) ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_in'( X ), Z ), T ) ) ] )
% 1.18/1.63 , clause( 1596, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL(
% 1.18/1.63 hAPP( 'c_Finite__Set_Ofold__graph'( 'c_HOL_Oplus__class_Oplus'( X ), Y,
% 1.18/1.63 hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), 'c_HOL_Ominus__class_Ominus'( T,
% 1.18/1.63 hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_bool' ) ) ), X, X ), U ) )
% 1.18/1.63 , hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_in'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ), U ) ) ) ] )
% 1.18/1.63 , clause( 1597, [ =( 'c_Map_Orestrict__map'( 'c_Fun_Ofun__upd'( X, Y, Z, T
% 1.18/1.63 , 'tc_Option_Ooption'( U ) ), W, T, U ), 'c_Fun_Ofun__upd'(
% 1.18/1.63 'c_Map_Orestrict__map'( X, 'c_HOL_Ominus__class_Ominus'( W, hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( T ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.18/1.63 'tc_bool' ) ) ), 'tc_fun'( T, 'tc_bool' ) ), T, U ), Y, Z, T,
% 1.18/1.63 'tc_Option_Ooption'( U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), W )
% 1.18/1.63 ) ) ] )
% 1.18/1.63 , clause( 1598, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ),
% 1.18/1.63 hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.63 X ), Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.18/1.63 'c_HOL_Ominus__class_Ominus'( T, hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.18/1.63 , 'tc_bool' ) ) ), X, X ), U ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), T
% 1.18/1.63 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.63 'c_Finite__Set_Ofold__graph'( 'c_HOL_Otimes__class_Otimes'( X ), Z, T, X
% 1.18/1.63 , X ), U ) ) ) ] )
% 1.18/1.63 , clause( 1599, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.18/1.63 =( 'c_Complete__Lattice_OSup__class_OSup'( hAPP( hAPP( 'c_Set_Oinsert'( X
% 1.18/1.63 ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ),
% 1.18/1.63 'c_Complete__Lattice_OSup__class_OSup'( Z, X ) ) ) ] )
% 1.18/1.63 , clause( 1600, [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.18/1.63 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1601, [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.63 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ), hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ] )
% 1.18/1.63 , clause( 1602, [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.63 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1603, [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.18/1.63 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ] )
% 1.18/1.63 , clause( 1604, [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.18/1.63 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~( hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1605, [ =( 'c_Finite__Set_Ofold'( X, Y, hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( Z ), T ), U ), Z, W ), hAPP( hAPP( X, T ),
% 1.18/1.63 'c_Finite__Set_Ofold'( X, Y, 'c_HOL_Ominus__class_Ominus'( U, hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( Z ), T ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.18/1.63 'tc_bool' ) ) ), 'tc_fun'( Z, 'tc_bool' ) ), Z, W ) ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( U, Z ) ), ~( 'c_Finite__Set_Ofun__left__comm'( X
% 1.18/1.63 , Z, W ) ) ] )
% 1.18/1.63 , clause( 1606, [ =( 'c_Finite__Set_Ocard'( hAPP( hAPP( 'c_Set_Oinsert'( X
% 1.18/1.63 ), Y ), Z ), X ), 'c_Suc'( 'c_Finite__Set_Ocard'(
% 1.18/1.63 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.18/1.63 , 'tc_bool' ) ), X ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.18/1.63 , clause( 1607, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( X ), hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.63 'c_Orderings_Oord__class_Omin'( X ), X ), Y ) ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_lessequals'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X
% 1.18/1.63 ), T ), Y ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.18/1.63 , clause( 1608, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.18/1.63 X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.18/1.63 Y ), hAPP( 'c_Finite__Set_Ofold1'( 'c_Orderings_Oord__class_Omin'( X ), X
% 1.18/1.63 ), T ) ) ) ), =( T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( T, X ) ) ] )
% 1.18/1.63 , clause( 1609, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.63 'c_Orderings_Oord__class_Omin'( X ), X ), Y ) ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_in'( X ), T ), Y ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.18/1.63 X, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.18/1.63 , clause( 1610, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.18/1.63 X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP(
% 1.18/1.63 'c_Finite__Set_Ofold1'( 'c_Lattices_Olower__semilattice__class_Oinf'( X )
% 1.18/1.63 , X ), T ) ) ) ), =( T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( T, X ) ) ] )
% 1.18/1.63 , clause( 1611, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.18/1.63 hAPP( 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X ),
% 1.18/1.63 hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), 'c_Finite__Set_Ofold'(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y, Z, X, X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_in'( X ), Y ), Z ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.18/1.63 , clause( 1612, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.18/1.63 hAPP( 'c_Finite__Set_Ofold1'( 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP(
% 1.18/1.63 hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), 'c_Finite__Set_Ofold'(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ), hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_in'( X ), Y ), Z ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.18/1.63 , clause( 1613, [ =( X, hAPP( 'c_Option_Ooption_OSome'( Y ), Z ) ), ~(
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), 'c_Option_Oset'( X, Y ) ) ) ) ] )
% 1.18/1.63 , clause( 1614, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Option_Oset'(
% 1.18/1.63 hAPP( 'c_Option_Ooption_OSome'( X ), Y ), X ) ) ) ] )
% 1.18/1.63 , clause( 1615, [ =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.18/1.63 , clause( 1616, [ ~( =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.18/1.63 ), =( 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ), Y
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1617, [ =( hAPP( 'c_Map_Orestrict__map'( X, Y, Z, T ), U ),
% 1.18/1.63 'c_Option_Ooption_ONone'( T ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), Y )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1618, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =(
% 1.18/1.63 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ), Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y,
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( Y, X ) ), =( hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.63 'c_Finite__Set_Ofold1'( 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ) ), hAPP(
% 1.18/1.63 'c_Finite__Set_Ofold1'( 'c_HOL_Oplus__class_Oplus'( X ), X ), Z ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1619, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), ~(
% 1.18/1.63 =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X
% 1.18/1.63 , 'tc_bool' ) ), Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y,
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( Y, X ) ), =( hAPP( 'c_Finite__Set_Ofold1'(
% 1.18/1.63 'c_HOL_Otimes__class_Otimes'( X ), X ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.18/1.63 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X ), Y ) ),
% 1.18/1.63 hAPP( 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X ), Z )
% 1.18/1.63 ) ) ] )
% 1.18/1.63 , clause( 1620, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.18/1.63 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.63 Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ), T ) ) ) ] )
% 1.18/1.63 , clause( 1621, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ), T
% 1.18/1.63 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y
% 1.18/1.63 ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X
% 1.18/1.63 , 'tc_bool' ) ), Z ), T ) ) ) ) ] )
% 1.18/1.63 , clause( 1622, [ =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.63 Z ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y
% 1.18/1.63 ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1623, [ =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ), hAPP(
% 1.18/1.63 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.18/1.63 'tc_bool' ) ), Y ), Z ) ), Y ) ] )
% 1.18/1.63 , clause( 1624, [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.63 , Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.63 , 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.18/1.63 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Y, 'tc_bool' ) ) ) ) ] )
% 1.18/1.63 , clause( 1625, [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.63 , Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.18/1.63 , 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.18/1.63 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Y, 'tc_bool' ) ) ) ) ] )
% 1.18/1.63 , clause( 1626, [ =( 'c_Option_Oset'( 'c_Option_Ooption_ONone'( X ), X ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.18/1.63 , clause( 1627, [ ~( =( 'c_Option_Oset'( X, Y ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ), =( X,
% 1.18/1.63 'c_Option_Ooption_ONone'( Y ) ) ] )
% 1.18/1.63 , clause( 1628, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.18/1.63 'c_Complete__Lattice_OInf__class_OInf'( Y, X ) ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.63 hAPP( 'c_in'( X ), Z ), Y ) ) ) ] )
% 1.18/1.63 , clause( 1629, [ =( hAPP( hAPP( X, Y ), hAPP( Z, T ) ),
% 1.18/1.63 'c_Finite__Set_Ofold'( X, Y, T, U, U ) ), ~( 'c_Finite__Set_Ofinite'( T,
% 1.18/1.63 U ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W, Z, V0, V1, V2, X,
% 1.18/1.63 V3, V4, U ) ) ] )
% 1.18/1.63 , clause( 1630, [ =( hAPP( hAPP( X, Y ), hAPP( Z, T ) ),
% 1.18/1.63 'c_Finite__Set_Ofold'( X, Y, T, U, U ) ), ~( 'c_Finite__Set_Ofinite'( T,
% 1.18/1.63 U ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( Z, W, V0, V1, X, V2,
% 1.18/1.63 V3, V4, U ) ) ] )
% 1.18/1.63 , clause( 1631, [ =( hAPP( X, Y ), 'c_Finite__Set_Ofold'( Z, T, Y, U, U ) )
% 1.18/1.63 , ~( 'c_Finite__Set_Ofinite'( Y, U ) ), ~(
% 1.18/1.63 'c_Complete__Lattice_Ocomplete__lattice'( W, X, V0, V1, V2, Z, T, V3, U )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1632, [ =( hAPP( X, Y ), 'c_Finite__Set_Ofold'( Z, T, Y, U, U ) )
% 1.18/1.63 , ~( 'c_Finite__Set_Ofinite'( Y, U ) ), ~(
% 1.18/1.63 'c_Complete__Lattice_Ocomplete__lattice'( X, W, V0, V1, Z, V2, V3, T, U )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1633, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.18/1.63 =( 'c_Complete__Lattice_OInf__class_OInf'( hAPP( hAPP( 'c_Set_Oinsert'( X
% 1.18/1.63 ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ),
% 1.18/1.63 'c_Complete__Lattice_OInf__class_OInf'( Z, X ) ) ) ] )
% 1.18/1.63 , clause( 1634, [ =( 'c_Map_Omap__add'( X, 'c_Fun_Ofun__upd'( Y, Z, hAPP(
% 1.18/1.63 'c_Option_Ooption_OSome'( T ), U ), W, 'tc_Option_Ooption'( T ) ), W, T )
% 1.18/1.63 , 'c_Fun_Ofun__upd'( 'c_Map_Omap__add'( X, Y, W, T ), Z, hAPP(
% 1.18/1.63 'c_Option_Ooption_OSome'( T ), U ), W, 'tc_Option_Ooption'( T ) ) ) ] )
% 1.18/1.63 , clause( 1635, [ =( 'c_Map_Omap__add'( 'c_COMBK'( 'c_Option_Ooption_ONone'(
% 1.18/1.63 X ), 'tc_Option_Ooption'( X ), Y ), Z, Y, X ), Z ) ] )
% 1.18/1.63 , clause( 1636, [ =( 'c_Map_Omap__add'( X, 'c_COMBK'(
% 1.18/1.63 'c_Option_Ooption_ONone'( Y ), 'tc_Option_Ooption'( Y ), Z ), Z, Y ), X )
% 1.18/1.63 ] )
% 1.18/1.63 , clause( 1637, [ 'c_Map_Omap__le'( 'c_Fun_Ofun__upd'( X, Y,
% 1.18/1.63 'c_Option_Ooption_ONone'( Z ), T, 'tc_Option_Ooption'( Z ) ), X, T, Z ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1638, [ 'c_Map_Omap__le'( 'c_COMBK'( 'c_Option_Ooption_ONone'( X
% 1.18/1.63 ), 'tc_Option_Ooption'( X ), Y ), Z, Y, X ) ] )
% 1.18/1.63 , clause( 1639, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.18/1.63 ) ), 'c_Map_Odom'( Y, X, Z ) ), 'c_Map_Odom'( T, X, Z ) ) ), ~(
% 1.18/1.63 'c_Map_Omap__le'( Y, T, X, Z ) ) ] )
% 1.18/1.63 , clause( 1640, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.18/1.63 'c_Finite__Set_Olinorder__class_OMax'( X ), 'c_Finite__Set_Ofold1'(
% 1.18/1.63 'c_Orderings_Oord__class_Omax'( X ), X ) ) ] )
% 1.18/1.63 , clause( 1641, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.18/1.63 'c_Finite__Set_Olinorder__class_OMin'( X ), 'c_Finite__Set_Ofold1'(
% 1.18/1.63 'c_Orderings_Oord__class_Omin'( X ), X ) ) ] )
% 1.18/1.63 , clause( 1642, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.18/1.63 'tc_bool' ) ), X ) ] )
% 1.18/1.63 , clause( 1643, [ 'c_Finite__Set_Ofinite'( 'c_Orderings_Obot__class_Obot'(
% 1.18/1.63 'tc_fun'( X, 'tc_bool' ) ), X ) ] )
% 1.18/1.63 , clause( 1644, [ ~( =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.18/1.63 ), =( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1645, [ ~( =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.18/1.63 ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1646, [ =( 'c_Set_Ovimage'( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ),
% 1.18/1.63 Z ), T ), U, Y ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.18/1.63 , 'c_Set_Ovimage'( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), U, Y ) ),
% 1.18/1.63 'c_Set_Ovimage'( X, T, U, Y ) ) ) ] )
% 1.18/1.63 , clause( 1647, [ =( hAPP( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), T ) )
% 1.18/1.63 , hAPP( hAPP( U, Z ), hAPP( X, T ) ) ), ~(
% 1.18/1.63 'c_Complete__Lattice_Ocomplete__lattice'( X, W, V0, V1, U, V2, V3, V4, Y
% 1.18/1.63 ) ) ] )
% 1.18/1.63 , clause( 1648, [ =( hAPP( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), T ) )
% 1.18/1.63 , hAPP( hAPP( U, Z ), hAPP( X, T ) ) ), ~(
% 1.18/1.63 'c_Complete__Lattice_Ocomplete__lattice'( W, X, V0, V1, V2, U, V3, V4, Y
% 1.18/1.63 ) ) ] )
% 1.18/1.63 , clause( 1649, [ 'c_Finite__Set_Ofinite'( hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.18/1.63 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.18/1.63 , clause( 1650, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), X ), Y )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1651, [ =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( X ), Z ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1652, [ =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Z ), T ) ) ) ] )
% 1.18/1.63 , clause( 1653, [ ~( =( hAPP( X, Y ), 'c_Option_Ooption_ONone'( Z ) ) ),
% 1.18/1.63 =( 'c_HOL_Ominus__class_Ominus'( 'c_Map_Odom'( X, T, Z ), hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( T ), Y ), U ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.18/1.63 'c_HOL_Ominus__class_Ominus'( 'c_Map_Odom'( X, T, Z ), U, 'tc_fun'( T,
% 1.18/1.63 'tc_bool' ) ) ) ] )
% 1.18/1.63 , clause( 1654, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSemi'( Y, Z )
% 1.18/1.63 ) ) ] )
% 1.18/1.63 , clause( 1655, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OBODY'( Z )
% 1.18/1.63 ) ) ] )
% 1.18/1.63 , clause( 1656, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OSemi'( X, Y ) ) )
% 1.18/1.63 ] )
% 1.18/1.63 , clause( 1657, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSKIP' ) )
% 1.18/1.63 ] )
% 1.18/1.63 , clause( 1658, [ 'c_Hoare__Mirabelle_Ohoare__valids'( X, Y, Z ), ~(
% 1.18/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ) ) ] )
% 1.18/1.63 , clause( 1659, [ hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSemi'(
% 1.18/1.63 X, Y ) ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( Y ), U )
% 1.18/1.63 , T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( X ), Z ), U ) ) ) ]
% 1.18/1.63 )
% 1.18/1.63 , clause( 1660, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( X ), Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ),
% 1.18/1.63 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.63 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.18/1.63 , clause( 1661, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( X ), Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'(
% 1.18/1.63 X, 'tc_bool' ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ] )
% 1.18/1.63 , clause( 1662, [ =( hAPP( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ), Z ), ~(
% 1.18/1.63 'c_Complete__Lattice_Ocomplete__lattice'( X, T, U, W, V0, V1, V2, V3, Y )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1663, [ =( hAPP( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ), Z ), ~(
% 1.18/1.63 'c_Complete__Lattice_Ocomplete__lattice'( T, X, U, W, V0, V1, V2, V3, Y )
% 1.18/1.63 ) ] )
% 1.18/1.63 , clause( 1664, [ hBOOL( hAPP( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.63 'c_Nitpick_Osko__Nitpick__XEx1__def__1__3'( hAPP( hAPP( 'c_Set_Oinsert'(
% 1.18/1.63 X ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), X
% 1.18/1.63 ) ) ) ] )
% 1.18/1.63 , clause( 1665, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.18/1.63 'c_Finite__Set_Osetsum'( Y, 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( T ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.18/1.63 'tc_bool' ) ) ), 'tc_fun'( T, 'tc_bool' ) ), T, X ),
% 1.18/1.63 'c_HOL_Ominus__class_Ominus'( 'c_Finite__Set_Osetsum'( Y, Z, T, X ), hAPP(
% 1.18/1.63 Y, U ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), U ), Z ) ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( Z, T ) ) ] )
% 1.18/1.63 , clause( 1666, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.18/1.63 'c_Finite__Set_Osetsum'( Y, 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( T ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.18/1.63 'tc_bool' ) ) ), 'tc_fun'( T, 'tc_bool' ) ), T, X ),
% 1.18/1.63 'c_HOL_Ominus__class_Ominus'( 'c_Finite__Set_Osetsum'( Y, Z, T, X ), hAPP(
% 1.18/1.63 Y, U ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), U ), Z ) ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( Z, T ) ) ] )
% 1.18/1.63 , clause( 1667, [ ~( =( hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.18/1.63 ), =( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.18/1.63 ~( 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y,
% 1.18/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( Y, X ) ), ~(
% 1.18/1.63 'c_OrderedGroup_Oab__semigroup__mult'( T, X ) ), =( hAPP(
% 1.18/1.63 'c_Finite__Set_Ofold1'( T, X ), hAPP( hAPP(
% 1.18/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.18/1.63 , Y ), Z ) ), hAPP( hAPP( T, hAPP( 'c_Finite__Set_Ofold1'( T, X ), Y ) )
% 1.18/1.63 , hAPP( 'c_Finite__Set_Ofold1'( T, X ), Z ) ) ) ] )
% 1.18/1.63 , clause( 1668, [ =( hAPP( 'c_Finite__Set_Ofold1'( X, Y ), hAPP( hAPP(
% 1.18/1.63 'c_Set_Oinsert'( Y ), Z ), T ) ), 'c_Finite__Set_Ofold'( X, Z, T, Y, Y )
% 1.18/1.63 ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), T ) ), ~(
% 1.18/1.63 'c_Finite__Set_Ofinite'( T, Y ) ), ~(
% 1.18/1.63 'c_OrderedGroup_Oab__semigroup__mult'( X, Y ) ) ] )
% 1.18/1.63 , clause( 1669, [ hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y, hAPP(
% 1.18/1.63 hAPP( 'c_Set_Oinsert'( Z ), T ), 'c_HOL_Ominus__class_Ominus'( U, hAPP(
% 1.18/1.63 hAPP( 'c_Set_Oinsert'( Z ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.18/1.63 Z, 'tc_bool' ) ) ), 'tc_fun'( Z, 'tc_bool' ) ) ), Z, Z ), W ) ), hBOOL(
% 1.18/1.63 hAPP( hAPP( 'c_in'( Z ), T ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y
% 1.18/1.63 ), U ) ) ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, T, U, Z, Z
% 1.23/1.63 ), W ) ) ), ~( 'c_OrderedGroup_Oab__semigroup__mult'( X, Z ) ) ] )
% 1.23/1.63 , clause( 1670, [ =( 'c_Map_Odom'( 'c_Fun_Ofun__upd'( X, Y,
% 1.23/1.63 'c_Option_Ooption_ONone'( Z ), T, 'tc_Option_Ooption'( Z ) ), T, Z ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'c_Map_Odom'( X, T, Z ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( T ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.23/1.63 'tc_bool' ) ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.23/1.63 , clause( 1671, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 hAPP( 'c_Finite__Set_Ofold1'( 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP(
% 1.23/1.63 hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( 'c_Finite__Set_Ofold1'(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Z ) ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.63 X ), Y ), Z ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), =( Z,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.23/1.63 , clause( 1672, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.23/1.63 hAPP( 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X ),
% 1.23/1.63 hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 'c_Finite__Set_Ofold1'(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), X ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( X ), Y ), Z ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), =( Z,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.23/1.63 , clause( 1673, [ =( 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'( X
% 1.23/1.63 , hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( Y, 'tc_bool' ) ) ), 'tc_fun'( Y, 'tc_bool' ) ), Y ),
% 1.23/1.63 'c_Finite__Set_Ocard'( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), X )
% 1.23/1.63 ), ~( 'c_Finite__Set_Ofinite'( X, Y ) ) ] )
% 1.23/1.63 , clause( 1674, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( T ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.23/1.63 'tc_bool' ) ) ), 'tc_fun'( T, 'tc_bool' ) ), T, X ),
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, Z, T, X ) ), hBOOL( hAPP( hAPP( 'c_in'( T ),
% 1.23/1.63 U ), Z ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ) ] )
% 1.23/1.63 , clause( 1675, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'(
% 1.23/1.63 X, hAPP( hAPP( 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) )
% 1.23/1.63 , 'c_Hoare__Mirabelle_Otriple_Otriple'( 'c_COMBK'( hAPP( 'c_COMBC'(
% 1.23/1.63 'c_fequal'( 'tc_Com_Ostate' ), 'tc_Com_Ostate', 'tc_Com_Ostate',
% 1.23/1.63 'tc_bool' ), 'v_sko__Hoare__Mirabelle__Xescape__2'( X, Y, T, Z ) ),
% 1.23/1.63 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 't_a' ), Z, 'c_COMBK'( hAPP( T,
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xescape__1'( X, Y, T, Z ) ), 'tc_fun'(
% 1.23/1.63 'tc_Com_Ostate', 'tc_bool' ), 't_a' ), 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ] )
% 1.23/1.63 , clause( 1676, [ =( 'c_Map_Omap__add'( 'c_Fun_Ofun__upd'( X, Y, hAPP(
% 1.23/1.63 'c_Option_Ooption_OSome'( Z ), T ), U, 'tc_Option_Ooption'( Z ) ), W, U,
% 1.23/1.63 Z ), 'c_Fun_Ofun__upd'( 'c_Map_Omap__add'( X, W, U, Z ), Y, hAPP(
% 1.23/1.63 'c_Option_Ooption_OSome'( Z ), T ), U, 'tc_Option_Ooption'( Z ) ) ),
% 1.23/1.63 hBOOL( hAPP( hAPP( 'c_in'( U ), Y ), 'c_Map_Odom'( W, U, Z ) ) ) ] )
% 1.23/1.63 , clause( 1677, [ =( 'c_Hoare__Mirabelle_OMGT'( 'v_c' ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( 'c_fequal'( 'tc_Com_Ostate' ),
% 1.23/1.63 'v_c', 'c_Natural_Oevalc'( 'v_c' ), 'tc_Com_Ostate' ) ) ] )
% 1.23/1.63 , clause( 1678, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.23/1.63 'c_Finite__Set_Olinorder__class_OMax'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), Z ) ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), hAPP(
% 1.23/1.63 'c_Finite__Set_Olinorder__class_OMax'( X ), Y ) ), hAPP(
% 1.23/1.63 'c_Finite__Set_Olinorder__class_OMax'( X ), Z ) ) ), =( Z,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.23/1.63 , clause( 1679, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.23/1.63 'c_Finite__Set_Olinorder__class_OMin'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), Z ) ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), hAPP(
% 1.23/1.63 'c_Finite__Set_Olinorder__class_OMin'( X ), Y ) ), hAPP(
% 1.23/1.63 'c_Finite__Set_Olinorder__class_OMin'( X ), Z ) ) ), =( Z,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.23/1.63 , clause( 1680, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.23/1.63 'c_Finite__Set_Olinorder__class_OMin'( X ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 X ), Y ), Z ) ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y ),
% 1.23/1.63 hAPP( 'c_Finite__Set_Olinorder__class_OMin'( X ), Z ) ) ), =( Z,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.23/1.63 , clause( 1681, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.23/1.63 'c_Finite__Set_Olinorder__class_OMax'( X ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 X ), Y ), Z ) ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y ),
% 1.23/1.63 hAPP( 'c_Finite__Set_Olinorder__class_OMax'( X ), Z ) ) ), =( Z,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.23/1.63 , clause( 1682, [ =( 'c_Finite__Set_Ofold__image'( X, Y, Z, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( T ), U ), W ), V0, T ), hAPP( hAPP( X, hAPP( Y, U ) ),
% 1.23/1.63 'c_Finite__Set_Ofold__image'( X, Y, Z, W, V0, T ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( T ), U ), W ) ), ~( 'c_Finite__Set_Ofinite'( W, T ) ), ~(
% 1.23/1.63 'c_OrderedGroup_Oab__semigroup__mult'( X, V0 ) ) ] )
% 1.23/1.63 , clause( 1683, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 1.23/1.63 , =( hAPP( 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X )
% 1.23/1.63 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.63 , hAPP( 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X ), Y
% 1.23/1.63 ) ), hAPP( 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X
% 1.23/1.63 ), Z ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.23/1.63 ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.23/1.63 , clause( 1684, [ =( hAPP( 'c_Finite__Set_Ofold1'( X, Y ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.23/1.63 , Z ), T ) ), hAPP( hAPP( X, hAPP( 'c_Finite__Set_Ofold1'( X, Y ), Z ) )
% 1.23/1.63 , hAPP( 'c_Finite__Set_Ofold1'( X, Y ), T ) ) ), =( T,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( T, Y ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ), ~(
% 1.23/1.63 'c_OrderedGroup_Oab__semigroup__idem__mult'( X, Y ) ) ] )
% 1.23/1.63 , clause( 1685, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 1.23/1.63 , =( hAPP( 'c_Finite__Set_Ofold1'( 'c_HOL_Otimes__class_Otimes'( X ), X )
% 1.23/1.63 , hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 'c_Finite__Set_Ofold1'(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), X ), Z ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( Z, X ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.23/1.63 , clause( 1686, [ =( hAPP( 'c_Finite__Set_Ofold1'( X, Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( Y ), Z ), T ) ), hAPP( hAPP( X, Z ), hAPP(
% 1.23/1.63 'c_Finite__Set_Ofold1'( X, Y ), T ) ) ), ~( 'c_Finite__Set_Ofinite'( T, Y
% 1.23/1.63 ) ), =( T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) )
% 1.23/1.63 , ~( 'c_OrderedGroup_Oab__semigroup__idem__mult'( X, Y ) ) ] )
% 1.23/1.63 , clause( 1687, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( T ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.23/1.63 'c_Finite__Set_Ofold1'( W, T ), U ) ) ) ), =( U,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( U, T ) ), ~( 'c_Lattices_Olower__semilattice'( X
% 1.23/1.63 , V0, W, T ) ) ] )
% 1.23/1.63 , clause( 1688, [ hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y, Z, T, U
% 1.23/1.63 ), hAPP( hAPP( X, W ), V0 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), W )
% 1.23/1.63 , Z ) ) ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y,
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_Set_Oinsert'( T ), W ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ), 'tc_fun'( T
% 1.23/1.63 , 'tc_bool' ) ), T, U ), V0 ) ) ) ] )
% 1.23/1.63 , clause( 1689, [ =( 'c_Finite__Set_Osetsum'( X,
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP( 'c_Set_Oinsert'( Z ), T ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ), 'tc_fun'( Z
% 1.23/1.63 , 'tc_bool' ) ), Z, 'tc_nat' ), 'c_Finite__Set_Osetsum'( X, Y, Z,
% 1.23/1.63 'tc_nat' ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), Y ) ) ] )
% 1.23/1.63 , clause( 1690, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X
% 1.23/1.63 , 'tc_bool' ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~(
% 1.23/1.63 hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.23/1.63 , 'tc_bool' ) ) ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ] )
% 1.23/1.63 , clause( 1691, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X
% 1.23/1.63 , 'tc_bool' ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~(
% 1.23/1.63 hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.23/1.63 , 'tc_bool' ) ) ), T ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), T ) ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1692, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X
% 1.23/1.63 , 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_bool' ) ) ), T ) ), ~( hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_in'( X ), Z ), Y ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), T )
% 1.23/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ) ) ] )
% 1.23/1.63 , clause( 1693, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.23/1.63 ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_in'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.23/1.63 'tc_fun'( X, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_bool' ) ) ), T ) ) ) ] )
% 1.23/1.63 , clause( 1694, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.23/1.63 ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_in'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.23/1.63 'tc_fun'( X, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_bool' ) ) ), T ) ) ) ] )
% 1.23/1.63 , clause( 1695, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.23/1.63 ) ), 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP( 'c_Set_Oinsert'( X ),
% 1.23/1.63 Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.23/1.63 'tc_fun'( X, 'tc_bool' ) ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z
% 1.23/1.63 ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.23/1.63 ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ) ) ] )
% 1.23/1.63 , clause( 1696, [ 'c_Nitpick_Ofold__graph_H'( X, Y, Z, hAPP( hAPP( X, T ),
% 1.23/1.63 U ), W, V0 ), ~( 'c_Nitpick_Ofold__graph_H'( X, Y,
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_Set_Oinsert'( W ), T ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( W, 'tc_bool' ) ) ), 'tc_fun'( W
% 1.23/1.63 , 'tc_bool' ) ), U, W, V0 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( W ), T ), Z
% 1.23/1.63 ) ) ) ] )
% 1.23/1.63 , clause( 1697, [ 'c_Map_Omap__le'( 'c_Fun_Ofun__upd'( X, Y,
% 1.23/1.63 'c_Option_Ooption_ONone'( Z ), T, 'tc_Option_Ooption'( Z ) ),
% 1.23/1.63 'c_Fun_Ofun__upd'( U, Y, hAPP( 'c_Option_Ooption_OSome'( Z ), W ), T,
% 1.23/1.63 'tc_Option_Ooption'( Z ) ), T, Z ), ~( 'c_Map_Omap__le'( X, U, T, Z ) ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1698, [ 'c_Map_Omap__le'( X, Y, Z, T ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.63 Z ), 'c_Map_Osko__Map__Xmap__le__def__1__1'( X, Y, Z, T ) ), 'c_Map_Odom'(
% 1.23/1.63 X, Z, T ) ) ) ] )
% 1.23/1.63 , clause( 1699, [ ~( =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , 'c_Map_Odom'( Y, X, Z ) ), 'c_Map_Odom'( T, X, Z ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), =(
% 1.23/1.63 'c_Map_Omap__add'( Y, T, X, Z ), 'c_Map_Omap__add'( T, Y, X, Z ) ) ] )
% 1.23/1.63 , clause( 1700, [ =( hAPP( 'c_Map_Omap__add'( X, Y, 't_a', Z ), 'v_x' ),
% 1.23/1.63 'c_Option_Ooption_Ooption__case'( hAPP( X, 'v_x' ),
% 1.23/1.63 'c_Option_Ooption_OSome'( Z ), hAPP( Y, 'v_x' ), 'tc_Option_Ooption'( Z )
% 1.23/1.63 , Z ) ) ] )
% 1.23/1.63 , clause( 1701, [ hBOOL( hAPP( 'c_Finite__Set_Ofold1Set'( X, Y, Z ),
% 1.23/1.63 'c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1'(
% 1.23/1.63 Y, X, Z ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.23/1.63 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ] )
% 1.23/1.63 , clause( 1702, [ hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Y, hAPP(
% 1.23/1.63 hAPP( 'c_Set_Oinsert'( Z ), T ), U ), Z, Z ), hAPP( hAPP( X, Y ), W ) ) )
% 1.23/1.63 , hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ), ~( hBOOL( hAPP(
% 1.23/1.63 'c_Finite__Set_Ofold__graph'( X, T, U, Z, Z ), W ) ) ), ~(
% 1.23/1.63 'c_OrderedGroup_Oab__semigroup__mult'( X, Z ) ) ] )
% 1.23/1.63 , clause( 1703, [ =( 'c_Map_Odom'( 'c_Fun_Ofun__upd'( X, Y, Z, T,
% 1.23/1.63 'tc_Option_Ooption'( U ) ), T, U ), hAPP( hAPP( 'c_Set_Oinsert'( T ), Y )
% 1.23/1.63 , 'c_Map_Odom'( X, T, U ) ) ), =( Z, 'c_Option_Ooption_ONone'( U ) ) ] )
% 1.23/1.63 , clause( 1704, [ hBOOL( hAPP( 'c_Finite__Set_Ofold1Set'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( Y ), Z ), T ), Y ), U ) ), hBOOL( hAPP( hAPP( 'c_in'( Y
% 1.23/1.63 ), Z ), T ) ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold__graph'( X, Z, T, Y
% 1.23/1.63 , Y ), U ) ) ) ] )
% 1.23/1.63 , clause( 1705, [ ~( =( 'c_Map_Odom'( X, Y, Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ), =( X,
% 1.23/1.63 'c_COMBK'( 'c_Option_Ooption_ONone'( Z ), 'tc_Option_Ooption'( Z ), Y ) )
% 1.23/1.63 ] )
% 1.23/1.63 , clause( 1706, [ =( 'c_Map_Odom'( 'c_COMBK'( 'c_Option_Ooption_ONone'( X )
% 1.23/1.63 , 'tc_Option_Ooption'( X ), Y ), Y, X ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( Y, 'tc_bool' ) ) ) ] )
% 1.23/1.63 , clause( 1707, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_lessequals'( X ), Y ), hAPP( 'c_Finite__Set_Olinorder__class_OMax'( X
% 1.23/1.63 ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.23/1.63 , clause( 1708, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_lessequals'( X ), hAPP( 'c_Finite__Set_Olinorder__class_OMin'( X ), Y
% 1.23/1.63 ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.23/1.63 , clause( 1709, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.23/1.63 'c_Finite__Set_Olinorder__class_OMin'( X ), Y ), Z ), ~( hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_in'( X ), Z ), Y ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.23/1.63 'c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1'( Y,
% 1.23/1.63 Z, X ) ), Y ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.23/1.63 , clause( 1710, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.23/1.63 'c_Finite__Set_Olinorder__class_OMax'( X ), Y ), Z ), ~( hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_in'( X ), Z ), Y ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.23/1.63 'c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1'( Y,
% 1.23/1.63 Z, X ) ), Y ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.23/1.63 , clause( 1711, [ =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ),
% 1.23/1.63 'c_Map_Osko__Map__XdomD__1__1'( Y, X, T, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( T ), Y ), 'c_Map_Odom'( X, T, Z ) ) ) ) ] )
% 1.23/1.63 , clause( 1712, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP(
% 1.23/1.63 'c_Finite__Set_Ofold1'( Y, X ), Z ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( X ), hAPP( hAPP( Y,
% 1.23/1.63 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1'(
% 1.23/1.63 Y, X ) ),
% 1.23/1.63 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2'(
% 1.23/1.63 Y, X ) ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ),
% 1.23/1.63 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1'(
% 1.23/1.63 Y, X ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ),
% 1.23/1.63 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2'(
% 1.23/1.63 Y, X ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) )
% 1.23/1.63 ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), ~(
% 1.23/1.63 'c_OrderedGroup_Oab__semigroup__mult'( Y, X ) ) ] )
% 1.23/1.63 , clause( 1713, [ =( hAPP( 'c_Map_Orestrict__map'( X,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' ) ), 't_a', Y
% 1.23/1.63 ), 'v_x' ), 'c_Option_Ooption_ONone'( Y ) ) ] )
% 1.23/1.63 , clause( 1714, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.23/1.63 =( 'c_Complete__Lattice_OInf__class_OInf'( hAPP( hAPP( 'c_Set_Oinsert'( X
% 1.23/1.63 ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), X ), hAPP(
% 1.23/1.63 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ) ] )
% 1.23/1.63 , clause( 1715, [ =( 'c_Finite__Set_Olattice_OSup__fin'( X, Y, Z ), hAPP( T
% 1.23/1.63 , Y ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.23/1.63 ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ), ~(
% 1.23/1.63 'c_Complete__Lattice_Ocomplete__lattice'( U, T, W, V0, V1, X, V2, V3, Z )
% 1.23/1.63 ) ] )
% 1.23/1.63 , clause( 1716, [ =( 'c_Finite__Set_Olattice_OInf__fin'( X, Y, Z ), hAPP( T
% 1.23/1.63 , Y ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.23/1.63 ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ), ~(
% 1.23/1.63 'c_Complete__Lattice_Ocomplete__lattice'( T, U, W, V0, X, V1, V2, V3, Z )
% 1.23/1.63 ) ] )
% 1.23/1.63 , clause( 1717, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.23/1.63 =( hAPP( 'c_Finite__Set_Olattice__class_OInf__fin'( X ), Y ),
% 1.23/1.63 'c_Complete__Lattice_OInf__class_OInf'( Y, X ) ), =( Y,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.23/1.63 , clause( 1718, [ ~( 'c_Orderings_Olinorder'( X, Y, Z ) ), =( hAPP(
% 1.23/1.63 'c_Finite__Set_Ofold1'( T, U ), hAPP( hAPP( 'c_Set_Oinsert'( U ), W ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ) ) ), W ) ] )
% 1.23/1.63 , clause( 1719, [ =( 'c_Option_Oset'( hAPP( 'c_Option_Ooption_OSome'( X ),
% 1.23/1.63 Y ), X ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ] )
% 1.23/1.63 , clause( 1720, [ =( 'c_Set_Ovimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_in'( Y ), X ), T ) ) ] )
% 1.23/1.63 , clause( 1721, [ hBOOL( hAPP( hAPP( X, hAPP( 'c_Finite__Set_Ofold1'( Y, Z
% 1.23/1.63 ), T ) ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), T ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( T, Z ) ), ~( 'c_Lattices_Olower__semilattice'( X
% 1.23/1.63 , W, Y, Z ) ) ] )
% 1.23/1.63 , clause( 1722, [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.23/1.63 'c_SetInterval_Oord__class_OlessThan'( Y, X ), 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( X, 'tc_bool' ) ) ) ) ] )
% 1.23/1.63 , clause( 1723, [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool'
% 1.23/1.63 ) ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ), ~( hBOOL(
% 1.23/1.63 hAPP( hAPP( 'c_lessequals'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.23/1.63 , 'tc_bool' ) ) ), T ) ) ) ] )
% 1.23/1.63 , clause( 1724, [ =( hAPP( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( 't_a', 'tc_bool'
% 1.23/1.63 ) ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool'
% 1.23/1.63 ), 'tc_bool' ), X ) ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'(
% 1.23/1.63 't_a', 'tc_bool' ), 'tc_bool' ), Y ) ), 'v_x' ), hAPP( hAPP( 'c_in'(
% 1.23/1.63 't_a' ), 'v_x' ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( 't_a', 'tc_bool'
% 1.23/1.63 ) ), X ), Y ) ) ) ] )
% 1.23/1.63 , clause( 1725, [ =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), Z ), 'c_Finite__Set_Ofold'( 'c_Set_Oinsert'( X ), Z, Y, X,
% 1.23/1.63 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.23/1.63 , clause( 1726, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.23/1.63 =( 'c_Complete__Lattice_OSup__class_OSup'( hAPP( hAPP( 'c_Set_Oinsert'( X
% 1.23/1.63 ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), X ), hAPP(
% 1.23/1.63 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ] )
% 1.23/1.63 , clause( 1727, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Ofold'( 'c_Lattices_Oupper__semilattice__class_Osup'( X )
% 1.23/1.63 , Y, hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), T ), X, X ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ),
% 1.23/1.63 'c_Finite__Set_Ofold'( 'c_Lattices_Oupper__semilattice__class_Osup'( X )
% 1.23/1.63 , Y, T, X, X ) ) ), ~( 'c_Finite__Set_Ofinite'( T, X ) ) ] )
% 1.23/1.63 , clause( 1728, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP(
% 1.23/1.63 'c_Finite__Set_Olattice__class_OInf__fin'( X ), Z ) ), Y ), ~( hBOOL(
% 1.23/1.63 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, X )
% 1.23/1.63 ) ] )
% 1.23/1.63 , clause( 1729, [ =( 'c_Finite__Set_Ocard'( hAPP( hAPP( 'c_Set_Oinsert'( X
% 1.23/1.63 ), Y ), Z ), X ), 'c_Finite__Set_Ocard'( Z, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( X ), Y ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.23/1.63 , clause( 1730, [ =( 'c_Map_Odom'( 'c_Fun_Ofun__upd'( 'c_COMBK'(
% 1.23/1.63 'c_Option_Ooption_ONone'( X ), 'tc_Option_Ooption'( X ), Y ), Z, hAPP(
% 1.23/1.63 'c_Option_Ooption_OSome'( X ), T ), Y, 'tc_Option_Ooption'( X ) ), Y, X )
% 1.23/1.63 , hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( Y, 'tc_bool' ) ) ) ) ] )
% 1.23/1.63 , clause( 1731, [ =( 'c_Fun_Ofun__upd'( 'c_Map_Orestrict__map'( X, Y, Z, T
% 1.23/1.63 ), U, 'c_Option_Ooption_ONone'( T ), Z, 'tc_Option_Ooption'( T ) ),
% 1.23/1.63 'c_Map_Orestrict__map'( X, 'c_HOL_Ominus__class_Ominus'( Y, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( Z ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.23/1.63 'tc_bool' ) ) ), 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ), ~( hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_in'( Z ), U ), Y ) ) ) ] )
% 1.23/1.63 , clause( 1732, [ =( 'c_Suc'( 'c_Finite__Set_Ocard'(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), 'tc_fun'( Y
% 1.23/1.63 , 'tc_bool' ) ), Y ) ), 'c_Finite__Set_Ocard'( X, Y ) ), ~( hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_in'( Y ), Z ), X ) ) ), ~( 'c_Finite__Set_Ofinite'( X, Y ) ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1733, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.23/1.63 , 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.23/1.63 'tc_bool' ) ) ), 'tc_fun'( Y, 'tc_bool' ) ), Y ) ), 'c_Finite__Set_Ocard'(
% 1.23/1.63 X, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), X ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( X, Y ) ) ] )
% 1.23/1.63 , clause( 1734, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetprod'( Y, 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( T ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.23/1.63 'tc_bool' ) ) ), 'tc_fun'( T, 'tc_bool' ) ), T, X ),
% 1.23/1.63 'c_Finite__Set_Osetprod'( Y, Z, T, X ) ), hBOOL( hAPP( hAPP( 'c_in'( T )
% 1.23/1.63 , U ), Z ) ), =( hAPP( Y, U ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( Z, T ) ) ] )
% 1.23/1.63 , clause( 1735, [ =( 'c_Finite__Set_Ofold'( X, Y, Z, T, U ), hAPP( hAPP( X
% 1.23/1.63 , W ), 'c_Finite__Set_Ofold'( X, Y, 'c_HOL_Ominus__class_Ominus'( Z, hAPP(
% 1.23/1.63 hAPP( 'c_Set_Oinsert'( T ), W ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.23/1.63 T, 'tc_bool' ) ) ), 'tc_fun'( T, 'tc_bool' ) ), T, U ) ) ), ~( hBOOL(
% 1.23/1.63 hAPP( hAPP( 'c_in'( T ), W ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, T )
% 1.23/1.63 ), ~( 'c_Finite__Set_Ofun__left__comm'( X, T, U ) ) ] )
% 1.23/1.63 , clause( 1736, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.23/1.63 , 'c_Finite__Set_Ocard'( 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), 'tc_fun'( Y
% 1.23/1.63 , 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'( Y ), T ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), 'tc_fun'( Y
% 1.23/1.63 , 'tc_bool' ) ), Y ) ), 'c_Finite__Set_Ocard'( X, Y ) ) ), ~( hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_in'( Y ), T ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ),
% 1.23/1.63 X ) ) ), ~( 'c_Finite__Set_Ofinite'( X, Y ) ) ] )
% 1.23/1.63 , clause( 1737, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, Z, T, X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, U ) ), 'c_Finite__Set_Osetsum'(
% 1.23/1.63 Y, 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_Set_Oinsert'( T ), U )
% 1.23/1.63 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ), 'tc_fun'(
% 1.23/1.63 T, 'tc_bool' ) ), T, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), U ), Z )
% 1.23/1.63 ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ) ] )
% 1.23/1.63 , clause( 1738, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_fun'( Y,
% 1.23/1.63 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.23/1.63 ) ] )
% 1.23/1.63 , clause( 1739, [ =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), Y ), Y )
% 1.23/1.63 ] )
% 1.23/1.63 , clause( 1740, [ =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), Y )
% 1.23/1.63 ] )
% 1.23/1.63 , clause( 1741, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.23/1.63 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.23/1.63 ) ) ) ] )
% 1.23/1.63 , clause( 1742, [ ~( hBOOL( hAPP( 'c_Finite__Set_Ofold1Set'( X,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ), Z ) ) )
% 1.23/1.63 ] )
% 1.23/1.63 , clause( 1743, [ =( hAPP( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.23/1.63 'tc_bool' ) ) ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( T, X,
% 1.23/1.63 U, W, V0, V1, Z, V2, Y ) ) ] )
% 1.23/1.63 , clause( 1744, [ =( hAPP( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.23/1.63 'tc_bool' ) ) ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X, T,
% 1.23/1.63 U, W, V0, V1, V2, Z, Y ) ) ] )
% 1.23/1.63 , clause( 1745, [ =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.23/1.63 , clause( 1746, [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( Y, 'tc_bool' ) ), Z, Y ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.23/1.63 , clause( 1747, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =( hAPP(
% 1.23/1.63 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.23/1.63 , clause( 1748, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =( hAPP(
% 1.23/1.63 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.23/1.63 , clause( 1749, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( X ) ), Y ) ] )
% 1.23/1.63 , clause( 1750, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( X ) ), Y ), Y ) ] )
% 1.23/1.63 , clause( 1751, [ =( hAPP( 'c_Finite__Set_Ofold1'( X, Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( Y ), Z ), T ) ), hAPP( hAPP( X, Z ), hAPP(
% 1.23/1.63 'c_Finite__Set_Ofold1'( X, Y ), T ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ),
% 1.23/1.63 Z ), T ) ), ~( 'c_Finite__Set_Ofinite'( T, Y ) ), =( T,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), ~(
% 1.23/1.63 'c_OrderedGroup_Oab__semigroup__mult'( X, Y ) ) ] )
% 1.23/1.63 , clause( 1752, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( X ), hAPP( 'c_Finite__Set_Olinorder__class_OMax'( X ), Y ) ), Y )
% 1.23/1.63 ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.23/1.63 ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.23/1.63 , clause( 1753, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( X ), hAPP( 'c_Finite__Set_Olinorder__class_OMin'( X ), Y ) ), Y )
% 1.23/1.63 ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.23/1.63 ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.23/1.63 , clause( 1754, [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL(
% 1.23/1.63 hAPP( hAPP( 'c_in'( U ), Y ), T ) ) ), ~(
% 1.23/1.63 'c_Complete__Lattice_Ocomplete__lattice'( W, Z, X, V0, V1, V2, V3, V4, U
% 1.23/1.63 ) ) ] )
% 1.23/1.63 , clause( 1755, [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL(
% 1.23/1.63 hAPP( hAPP( 'c_in'( U ), T ), Z ) ) ), ~(
% 1.23/1.63 'c_Complete__Lattice_Ocomplete__lattice'( Y, W, X, V0, V1, V2, V3, V4, U
% 1.23/1.63 ) ) ] )
% 1.23/1.63 , clause( 1756, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ),
% 1.23/1.63 ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) )
% 1.23/1.63 ) ] )
% 1.23/1.63 , clause( 1757, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ),
% 1.23/1.63 ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) )
% 1.23/1.63 ) ] )
% 1.23/1.63 , clause( 1758, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 1.23/1.63 T, X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) )
% 1.23/1.63 ] )
% 1.23/1.63 , clause( 1759, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 1.23/1.63 T, X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) )
% 1.23/1.63 ] )
% 1.23/1.63 , clause( 1760, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 1.23/1.63 T, X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) )
% 1.23/1.63 ] )
% 1.23/1.63 , clause( 1761, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL(
% 1.23/1.63 hAPP( hAPP( 'c_in'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y
% 1.23/1.63 ), Z ) ) ) ] )
% 1.23/1.63 , clause( 1762, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL(
% 1.23/1.63 hAPP( hAPP( 'c_in'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y
% 1.23/1.63 ), Z ) ) ) ] )
% 1.23/1.63 , clause( 1763, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.23/1.63 hAPP( hAPP( 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, T,
% 1.23/1.63 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.23/1.63 , clause( 1764, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.23/1.63 hAPP( hAPP( 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( T, Z,
% 1.23/1.63 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.23/1.63 , clause( 1765, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_in'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ), T ), Z ) ) ) ) ] )
% 1.23/1.63 , clause( 1766, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.23/1.63 , clause( 1767, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.23/1.63 , clause( 1768, [ 'c_Map_Omap__le'( 'c_Map_Omap__add'( X, Y, Z, T ), U, Z,
% 1.23/1.63 T ), ~( 'c_Map_Omap__le'( X, 'c_Map_Omap__add'( X, Y, Z, T ), Z, T ) ),
% 1.23/1.63 ~( 'c_Map_Omap__le'( Y, U, Z, T ) ), ~( 'c_Map_Omap__le'( X, U, Z, T ) )
% 1.23/1.63 ] )
% 1.23/1.63 , clause( 1769, [ 'c_Map_Omap__le'( X, 'c_Map_Omap__add'( Y, X, Z, T ), Z,
% 1.23/1.63 T ) ] )
% 1.23/1.63 , clause( 1770, [ ~( =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ),
% 1.23/1.63 T ) ) ), =( hAPP( 'c_Map_Omap__add'( U, X, W, Z ), Y ), hAPP(
% 1.23/1.63 'c_Option_Ooption_OSome'( Z ), T ) ) ] )
% 1.23/1.63 , clause( 1771, [ ~( =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ),
% 1.23/1.63 T ) ) ), =( hAPP( 'c_Map_Omap__add'( U, X, W, Z ), Y ), hAPP(
% 1.23/1.63 'c_Option_Ooption_OSome'( Z ), T ) ) ] )
% 1.23/1.63 , clause( 1772, [ ~( =( hAPP( X, Y ), 'c_Option_Ooption_ONone'( Z ) ) ),
% 1.23/1.63 ~( =( hAPP( T, Y ), 'c_Option_Ooption_ONone'( Z ) ) ), =( hAPP(
% 1.23/1.63 'c_Map_Omap__add'( X, T, U, Z ), Y ), 'c_Option_Ooption_ONone'( Z ) ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1773, [ =( 'c_Set_Ovimage'( X, hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.23/1.63 , Z ), T ), U, Y ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.23/1.63 , 'c_Set_Ovimage'( X, Z, U, Y ) ), 'c_Set_Ovimage'( X, T, U, Y ) ) ) ] )
% 1.23/1.63 , clause( 1774, [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ),
% 1.23/1.63 'c_Finite__Set_Ofinite'( Y, X ) ] )
% 1.23/1.63 , clause( 1775, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ] )
% 1.23/1.63 , clause( 1776, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ] )
% 1.23/1.63 , clause( 1777, [ =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.23/1.63 X, 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), Z ) ) ] )
% 1.23/1.63 , clause( 1778, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ) ) ] )
% 1.23/1.63 , clause( 1779, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), hAPP(
% 1.23/1.63 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ) ) ] )
% 1.23/1.63 , clause( 1780, [ =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.63 'tc_fun'( X, 'tc_bool' ) ), Z ), Y ) ) ] )
% 1.23/1.63 , clause( 1781, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) ) ] )
% 1.23/1.63 , clause( 1782, [ ~( 'class_HOL_Ominus'( X ) ), =( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( hAPP( Y, 'v_x' ), hAPP( Z, 'v_x' ), X ) ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1783, [ =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.23/1.63 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ), Y ), Z ) ) ] )
% 1.23/1.63 , clause( 1784, [ =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ), Z ),
% 1.23/1.63 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ), Y ), Z ) ) ] )
% 1.23/1.63 , clause( 1785, [ ~( =( hAPP( 'c_Map_Omap__add'( X, Y, Z, T ), U ),
% 1.23/1.63 'c_Option_Ooption_ONone'( T ) ) ), =( hAPP( Y, U ),
% 1.23/1.63 'c_Option_Ooption_ONone'( T ) ) ] )
% 1.23/1.63 , clause( 1786, [ ~( =( hAPP( 'c_Map_Omap__add'( X, Y, Z, T ), U ),
% 1.23/1.63 'c_Option_Ooption_ONone'( T ) ) ), =( hAPP( X, U ),
% 1.23/1.63 'c_Option_Ooption_ONone'( T ) ) ] )
% 1.23/1.63 , clause( 1787, [ ~( =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ),
% 1.23/1.63 T ) ) ), ~( =( hAPP( U, Y ), 'c_Option_Ooption_ONone'( Z ) ) ), =( hAPP(
% 1.23/1.63 'c_Map_Omap__add'( X, U, W, Z ), Y ), hAPP( 'c_Option_Ooption_OSome'( Z )
% 1.23/1.63 , T ) ) ] )
% 1.23/1.63 , clause( 1788, [ ~( =( hAPP( 'c_Map_Omap__add'( X, Y, Z, T ), U ), hAPP(
% 1.23/1.63 'c_Option_Ooption_OSome'( T ), W ) ) ), =( hAPP( X, U ), hAPP(
% 1.23/1.63 'c_Option_Ooption_OSome'( T ), W ) ), =( hAPP( Y, U ), hAPP(
% 1.23/1.63 'c_Option_Ooption_OSome'( T ), W ) ) ] )
% 1.23/1.63 , clause( 1789, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.23/1.63 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ] )
% 1.23/1.63 , clause( 1790, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ] )
% 1.23/1.63 , clause( 1791, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ] )
% 1.23/1.63 , clause( 1792, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.23/1.63 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ] )
% 1.23/1.63 , clause( 1793, [ =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.23/1.63 X, 'tc_bool' ) ), Z ), T ) ) ) ] )
% 1.23/1.63 , clause( 1794, [ =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.23/1.63 X, 'tc_bool' ) ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Z ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.23/1.63 X, 'tc_bool' ) ), Y ), T ) ) ) ] )
% 1.23/1.63 , clause( 1795, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.23/1.63 , T, X ) ) ), =( Z, T ) ] )
% 1.23/1.63 , clause( 1796, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.23/1.63 , T, X ) ) ), =( Y, Z ) ] )
% 1.23/1.63 , clause( 1797, [ ~( =( 'c_Option_Ooption_ONone'( X ), hAPP(
% 1.23/1.63 'c_Option_Ooption_OSome'( X ), Y ) ) ) ] )
% 1.23/1.63 , clause( 1798, [ ~( =( 'c_Option_Ooption_ONone'( X ), hAPP(
% 1.23/1.63 'c_Option_Ooption_OSome'( X ), Y ) ) ) ] )
% 1.23/1.63 , clause( 1799, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Y,
% 1.23/1.63 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 1.23/1.63 Z, 'tc_bool' ) ) ) ] )
% 1.23/1.63 , clause( 1800, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Y ), Y ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1801, [ =( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), Y ), Y ) ] )
% 1.23/1.63 , clause( 1802, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( 't_a', X ) ), Y )
% 1.23/1.63 , Z ), 'v_x' ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.63 X ), hAPP( Y, 'v_x' ) ), hAPP( Z, 'v_x' ) ) ) ] )
% 1.23/1.63 , clause( 1803, [ =( hAPP( 'c_Finite__Set_Ofold1'( X, Y ), Z ), 'c_The'(
% 1.23/1.63 'c_Finite__Set_Ofold1Set'( X, Z, Y ), Y ) ) ] )
% 1.23/1.63 , clause( 1804, [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X
% 1.23/1.63 , Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z )
% 1.23/1.63 ) ] )
% 1.23/1.63 , clause( 1805, [ =( 'c_Set_Ovimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.23/1.63 , 'tc_fun'( T, 'tc_bool' ) ), U, T ), 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.63 'c_Set_Ovimage'( X, Y, U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U
% 1.23/1.63 , 'tc_bool' ) ) ) ] )
% 1.23/1.63 , clause( 1806, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z,
% 1.23/1.63 T ) ) ), =( Y, T ) ] )
% 1.23/1.63 , clause( 1807, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z,
% 1.23/1.63 T ) ) ), =( X, Z ) ] )
% 1.23/1.63 , clause( 1808, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y
% 1.23/1.63 , 'tc_bool' ) ), Y ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ] )
% 1.23/1.63 , clause( 1809, [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X
% 1.23/1.63 , Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z )
% 1.23/1.63 ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ] )
% 1.23/1.63 , clause( 1810, [ 'c_Map_Omap__le'( X, Y, Z, T ), ~( 'c_Map_Omap__le'(
% 1.23/1.63 'c_Map_Omap__add'( U, X, Z, T ), Y, Z, T ) ) ] )
% 1.23/1.63 , clause( 1811, [ 'c_Map_Omap__le'( X, X, Y, Z ) ] )
% 1.23/1.63 , clause( 1812, [ 'c_Map_Omap__le'( X, Y, Z, T ), ~( 'c_Map_Omap__le'( U, Y
% 1.23/1.63 , Z, T ) ), ~( 'c_Map_Omap__le'( X, U, Z, T ) ) ] )
% 1.23/1.63 , clause( 1813, [ =( 'c_Map_Odom'( 'c_Map_Omap__add'( X, Y, Z, T ), Z, T )
% 1.23/1.63 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z,
% 1.23/1.63 'tc_bool' ) ), 'c_Map_Odom'( Y, Z, T ) ), 'c_Map_Odom'( X, Z, T ) ) ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1814, [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.23/1.63 , clause( 1815, [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.23/1.63 , clause( 1816, [ ~( =( hAPP( 'c_Option_Ooption_OSome'( X ), Y ),
% 1.23/1.63 'c_Option_Ooption_ONone'( X ) ) ) ] )
% 1.23/1.63 , clause( 1817, [ ~( =( hAPP( 'c_Option_Ooption_OSome'( X ), Y ),
% 1.23/1.63 'c_Option_Ooption_ONone'( X ) ) ) ] )
% 1.23/1.63 , clause( 1818, [ ~( =( hAPP( 'c_Option_Ooption_OSome'( X ), Y ), hAPP(
% 1.23/1.63 'c_Option_Ooption_OSome'( X ), Z ) ) ), =( Y, Z ) ] )
% 1.23/1.63 , clause( 1819, [ =( 'c_Map_Omap__add'( X, 'c_Map_Omap__add'( Y, Z, T, U )
% 1.23/1.63 , T, U ), 'c_Map_Omap__add'( 'c_Map_Omap__add'( X, Y, T, U ), Z, T, U ) )
% 1.23/1.63 ] )
% 1.23/1.63 , clause( 1820, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP(
% 1.23/1.63 hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ) ), ~(
% 1.23/1.63 'c_OrderedGroup_Oab__semigroup__mult'( X, U ) ) ] )
% 1.23/1.63 , clause( 1821, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 1.23/1.63 hAPP( X, Z ), hAPP( hAPP( X, Y ), T ) ) ), ~(
% 1.23/1.63 'c_OrderedGroup_Oab__semigroup__mult'( X, U ) ) ] )
% 1.23/1.63 , clause( 1822, [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ),
% 1.23/1.63 ~( 'c_OrderedGroup_Oab__semigroup__mult'( X, T ) ) ] )
% 1.23/1.63 , clause( 1823, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL(
% 1.23/1.63 hAPP( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.23/1.63 T, 'tc_bool' ) ), Z ), X ), Y ) ) ) ] )
% 1.23/1.63 , clause( 1824, [ hBOOL( hAPP( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), Z ), T ) ), ~( hBOOL( hAPP( Z, T ) ) ) ] )
% 1.23/1.63 , clause( 1825, [ hBOOL( hAPP( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , Y ), Z ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ] )
% 1.23/1.63 , clause( 1826, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.23/1.63 , X ), Z ), Y ) ) ] )
% 1.23/1.63 , clause( 1827, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.23/1.63 , Z ), X ), Y ) ) ] )
% 1.23/1.63 , clause( 1828, [ =( 'c_Map_Omap__add'( X, Y, Z, T ), 'c_Map_Omap__add'( Y
% 1.23/1.63 , X, Z, T ) ), ~( 'c_Map_Omap__le'( X, 'c_Map_Omap__add'( X, Y, Z, T ), Z
% 1.23/1.63 , T ) ) ] )
% 1.23/1.63 , clause( 1829, [ ~( =( 'c_Map_Omap__add'( X, Y, Z, T ), 'c_Map_Omap__add'(
% 1.23/1.63 Y, X, Z, T ) ) ), 'c_Map_Omap__le'( X, 'c_Map_Omap__add'( X, Y, Z, T ), Z
% 1.23/1.63 , T ) ] )
% 1.23/1.63 , clause( 1830, [ =( X, Y ), ~( 'c_Map_Omap__le'( Y, X, Z, T ) ), ~(
% 1.23/1.63 'c_Map_Omap__le'( X, Y, Z, T ) ) ] )
% 1.23/1.63 , clause( 1831, [ ~( =( hAPP( 'c_Map_Omap__add'( X, Y, Z, T ), U ), hAPP(
% 1.23/1.63 'c_Option_Ooption_OSome'( T ), W ) ) ), =( hAPP( Y, U ),
% 1.23/1.63 'c_Option_Ooption_ONone'( T ) ), =( hAPP( Y, U ), hAPP(
% 1.23/1.63 'c_Option_Ooption_OSome'( T ), W ) ) ] )
% 1.23/1.63 , clause( 1832, [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X
% 1.23/1.63 , Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_Set_Oinsert'( Z ), T ), Y
% 1.23/1.63 ), 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ] )
% 1.23/1.63 , clause( 1833, [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X
% 1.23/1.63 , hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), T ), 'tc_fun'( Y, 'tc_bool' ) )
% 1.23/1.63 , Y ), ~( 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 1.23/1.63 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ] )
% 1.23/1.63 , clause( 1834, [ hBOOL( hAPP( X, hAPP( Y, Z ) ) ), ~( hBOOL( hAPP(
% 1.23/1.63 'c_Set_Ovimage'( Y, X, T, U ), Z ) ) ) ] )
% 1.23/1.63 , clause( 1835, [ hBOOL( hAPP( 'c_Set_Ovimage'( X, Y, Z, T ), U ) ), ~(
% 1.23/1.63 hBOOL( hAPP( Y, hAPP( X, U ) ) ) ) ] )
% 1.23/1.63 , clause( 1836, [ =( 'c_The'( hAPP( 'c_fequal'( X ), Y ), X ), Y ) ] )
% 1.23/1.63 , clause( 1837, [ =( 'c_Option_Othe'( hAPP( 'c_Option_Ooption_OSome'( X ),
% 1.23/1.63 Y ), X ), Y ) ] )
% 1.23/1.63 , clause( 1838, [ hBOOL( hAPP( 'c_Finite__Set_Ofold1Set'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.23/1.63 'tc_bool' ) ) ), Y ), Z ) ) ] )
% 1.23/1.63 , clause( 1839, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.23/1.63 'c_Finite__Set_Olinorder__class_OMin'( X ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 X ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) )
% 1.23/1.63 , Y ) ] )
% 1.23/1.63 , clause( 1840, [ =( 'c_The'( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), X ), Y ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1841, [ =( hAPP( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), hAPP(
% 1.23/1.63 hAPP( 'c_Set_Oinsert'( Y ), T ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.23/1.63 Y, 'tc_bool' ) ) ) ) ), hAPP( hAPP( U, Z ), T ) ), ~(
% 1.23/1.63 'c_Complete__Lattice_Ocomplete__lattice'( X, W, V0, V1, U, V2, V3, V4, Y
% 1.23/1.63 ) ) ] )
% 1.23/1.63 , clause( 1842, [ =( hAPP( X, hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ), hAPP(
% 1.23/1.63 hAPP( 'c_Set_Oinsert'( Y ), T ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.23/1.63 Y, 'tc_bool' ) ) ) ) ), hAPP( hAPP( U, Z ), T ) ), ~(
% 1.23/1.63 'c_Complete__Lattice_Ocomplete__lattice'( W, X, V0, V1, V2, U, V3, V4, Y
% 1.23/1.63 ) ) ] )
% 1.23/1.63 , clause( 1843, [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( Y ), Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.23/1.63 'tc_bool' ) ) ), 'tc_fun'( Y, 'tc_bool' ) ), T, 'tc_fun'( Y, 'tc_bool' )
% 1.23/1.63 ) ) ] )
% 1.23/1.63 , clause( 1844, [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( Y ), Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 1.23/1.63 'tc_fun'( Y, 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'( Y ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), 'tc_fun'( Y
% 1.23/1.63 , 'tc_bool' ) ) ) ] )
% 1.23/1.63 , clause( 1845, [ =( X, Y ), ~( hBOOL( hAPP( 'c_Finite__Set_Ofold1Set'( Z,
% 1.23/1.63 hAPP( hAPP( 'c_Set_Oinsert'( T ), X ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( T, 'tc_bool' ) ) ), T ), Y ) ) ) ] )
% 1.23/1.63 , clause( 1846, [ =( 'c_Set_Ocontents'( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y
% 1.23/1.63 ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), X ), Y
% 1.23/1.63 ) ] )
% 1.23/1.63 , clause( 1847, [ =( X, 'c_Nitpick_Osko__Nitpick__XEx1__def__1__3'( hAPP(
% 1.23/1.63 hAPP( 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.23/1.63 Y, 'tc_bool' ) ) ), Y ) ), ~( hBOOL( hAPP( hAPP( hAPP( 'c_Set_Oinsert'( Y
% 1.23/1.63 ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), X
% 1.23/1.63 ) ) ) ] )
% 1.23/1.63 , clause( 1848, [ =( hAPP( 'c_Finite__Set_Ofold1'( X, Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.23/1.63 'tc_bool' ) ) ) ), Z ) ] )
% 1.23/1.63 , clause( 1849, [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP(
% 1.23/1.63 'c_Finite__Set_Olinorder__class_OMax'( X ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 X ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) )
% 1.23/1.63 , Y ) ] )
% 1.23/1.63 , clause( 1850, [ =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.23/1.63 , 'tc_bool' ) ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ) ] )
% 1.23/1.63 , clause( 1851, [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Y, X ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ) ) ] )
% 1.23/1.63 , clause( 1852, [ =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.63 , hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( X, 'tc_bool' ) ) ) ), Z ) ) ] )
% 1.23/1.63 , clause( 1853, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.23/1.63 =( 'c_Complete__Lattice_OInf__class_OInf'( hAPP( hAPP( 'c_Set_Oinsert'( X
% 1.23/1.63 ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), X
% 1.23/1.63 ), Y ) ] )
% 1.23/1.63 , clause( 1854, [ =( hAPP( 'c_Map_Omap__add'( X, Y, Z, T ), U ), hAPP( X, U
% 1.23/1.63 ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), 'c_Map_Odom'( Y, Z, T ) ) ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1855, [ =( hAPP( 'c_Map_Omap__add'( X, Y, Z, T ), U ), hAPP( Y, U
% 1.23/1.63 ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), 'c_Map_Odom'( X, Z, T ) ) ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1856, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Map_Odom'( Z, X,
% 1.23/1.63 T ) ) ), =( hAPP( Z, Y ), 'c_Option_Ooption_ONone'( T ) ) ] )
% 1.23/1.63 , clause( 1857, [ ~( =( hAPP( X, Y ), 'c_Option_Ooption_ONone'( Z ) ) ),
% 1.23/1.63 ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), 'c_Map_Odom'( X, T, Z ) ) ) ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1858, [ ~( =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ),
% 1.23/1.63 T ) ) ), hBOOL( hAPP( hAPP( 'c_in'( U ), Y ), 'c_Map_Odom'( X, U, Z ) ) )
% 1.23/1.63 ] )
% 1.23/1.63 , clause( 1859, [ =( hAPP( X, Y ), hAPP( Z, Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( T ), Y ), 'c_Map_Odom'( X, T, U ) ) ) ), ~( 'c_Map_Omap__le'( X,
% 1.23/1.63 Z, T, U ) ) ] )
% 1.23/1.63 , clause( 1860, [ =( hAPP( 'c_Map_Omap__add'( X, Y, Z, T ), U ), hAPP( Y, U
% 1.23/1.63 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), 'c_Map_Odom'( Y, Z, T ) ) )
% 1.23/1.63 ) ] )
% 1.23/1.63 , clause( 1861, [ ~( =( hAPP( X, Y ), hAPP( 'c_Option_Ooption_OSome'( Z ),
% 1.23/1.63 T ) ) ), =( hAPP( hAPP( 'c_Set_Oinsert'( U ), Y ), 'c_Map_Odom'( X, U, Z
% 1.23/1.63 ) ), 'c_Map_Odom'( X, U, Z ) ) ] )
% 1.23/1.63 , clause( 1862, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( U, W ),
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3'( X, Y, T, Z, V0, U
% 1.23/1.63 ) ) ), ~( hBOOL( hAPP( hAPP( V0, W ),
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2'( X, Y, T, Z ) ) ) )
% 1.23/1.63 , ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, Z, U, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ] )
% 1.23/1.63 , clause( 1863, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( U, W ),
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xconseq12__3'( Y, V0, T, U ) ) ), ~( hBOOL(
% 1.23/1.63 hAPP( hAPP( V0, W ), 'v_sko__Hoare__Mirabelle__Xconseq12__2'( Y, V0, T, U
% 1.23/1.63 ) ) ) ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, Z, U, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ] )
% 1.23/1.63 , clause( 1864, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( U, W ),
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3'( X, Y, T, Z, V0
% 1.23/1.63 , U ) ) ), ~( hBOOL( hAPP( hAPP( V0, W ),
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2'( X, Y, T, Z ) )
% 1.23/1.63 ) ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, Z, U, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ] )
% 1.23/1.63 , clause( 1865, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( Y,
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1'( X, Y, T, Z ) )
% 1.23/1.63 , 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2'( X, Y, T, Z )
% 1.23/1.63 ) ) ] )
% 1.23/1.63 , clause( 1866, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), ~( hBOOL( hAPP( hAPP( T,
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1'( X, Y, T, Z ) )
% 1.23/1.63 , 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3'( X, Y, T, Z, U
% 1.23/1.63 , W ) ) ) ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( U, Z, W, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ] )
% 1.23/1.63 , clause( 1867, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( Y,
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1'( X, Y, T, Z ) ),
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2'( X, Y, T, Z ) ) ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1868, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( U,
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xconseq2__1'( T, U ) ),
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xconseq2__2'( T, U ) ) ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, U, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ] )
% 1.23/1.63 , clause( 1869, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( Y,
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xconseq12__1'( Y, U, T, W ) ),
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xconseq12__2'( Y, U, T, W ) ) ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( U, Z, W, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ] )
% 1.23/1.63 , clause( 1870, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( Y,
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xconseq1__1'( Y, U ) ),
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xconseq1__2'( Y, U ) ) ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( U, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ] )
% 1.23/1.63 , clause( 1871, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), ~( hBOOL( hAPP( hAPP( T,
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1'( X, Y, T, Z ) ),
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3'( X, Y, T, Z, U, W )
% 1.23/1.63 ) ) ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( U, Z, W, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ] )
% 1.23/1.63 , clause( 1872, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), ~( hBOOL( hAPP( hAPP( U,
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xconseq1__1'( Y, U ) ),
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xconseq1__2'( Y, U ) ) ) ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( U, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ] )
% 1.23/1.63 , clause( 1873, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), ~( hBOOL( hAPP( hAPP( T,
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xconseq12__1'( Y, U, T, W ) ),
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xconseq12__3'( Y, U, T, W ) ) ) ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( U, Z, W, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ] )
% 1.23/1.63 , clause( 1874, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), ~( hBOOL( hAPP( hAPP( T,
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xconseq2__1'( T, U ) ),
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xconseq2__2'( T, U ) ) ) ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, U, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ) ) ] )
% 1.23/1.63 , clause( 1875, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 't_a' ), 'tc_bool' ) ) ), 't_a' ), hBOOL( hAPP( hAPP( Y,
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xescape__1'( X, Y, T, Z ) ),
% 1.23/1.63 'v_sko__Hoare__Mirabelle__Xescape__2'( X, Y, T, Z ) ) ) ] )
% 1.23/1.63 , clause( 1876, [ =( 'c_Hoare__Mirabelle_OMGT'( X ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( 'c_fequal'( 'tc_Com_Ostate' ), X,
% 1.23/1.63 'c_Natural_Oevalc'( X ), 'tc_Com_Ostate' ) ) ] )
% 1.23/1.63 , clause( 1877, [ =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.23/1.63 , 'tc_bool' ) ) ), Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1878, [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ),
% 1.23/1.63 Y ), 'c_Set_Ovimage'( X, hAPP( hAPP( 'c_Set_Oinsert'( U ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ) ), T, U ) ) )
% 1.23/1.63 ) ] )
% 1.23/1.63 , clause( 1879, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 1.23/1.63 hAPP( hAPP( 'c_Set_Oinsert'( T ), hAPP( Z, Y ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ), X, T ) ) )
% 1.23/1.63 ] )
% 1.23/1.63 , clause( 1880, [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL(
% 1.23/1.63 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~(
% 1.23/1.63 'c_OrderedGroup_Oab__semigroup__mult'( T, U ) ) ] )
% 1.23/1.63 , clause( 1881, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Y ), Z ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.23/1.63 , 'tc_bool' ) ), Z ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ] )
% 1.23/1.63 , clause( 1882, [ 'c_Hoare__Mirabelle_Ohoare__derivs'(
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 'tc_Com_Ostate' ), 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, 'tc_Com_Ostate' ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 'tc_Com_Ostate' ), 'tc_bool' ) ) ), 'tc_Com_Ostate' ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__valids'( 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) )
% 1.23/1.63 , hAPP( hAPP( 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 'tc_Com_Ostate' ) ), 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z,
% 1.23/1.63 'tc_Com_Ostate' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) ) ),
% 1.23/1.63 'tc_Com_Ostate' ) ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'(
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 'tc_Com_Ostate' ), 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_OMGT'( Y ) ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) )
% 1.23/1.63 ), 'tc_Com_Ostate' ) ) ] )
% 1.23/1.63 , clause( 1883, [ hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( 'c_Com_Ocom_OBODY'(
% 1.23/1.63 X ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'(
% 1.23/1.63 'c_Option_Othe'( hAPP( 'c_Com_Obody', X ), 'tc_Com_Ocom' ) ), Y ), Z ) )
% 1.23/1.63 ) ] )
% 1.23/1.63 , clause( 1884, [ hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( 'c_Option_Othe'(
% 1.23/1.63 hAPP( 'c_Com_Obody', X ), 'tc_Com_Ocom' ) ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_Natural_Oevalc'( 'c_Com_Ocom_OBODY'( X ) ), Y ), Z ) ) ) ] )
% 1.23/1.63 , clause( 1885, [ 'c_Finite__Set_Ofinite'( 'c_Map_Odom'( 'c_Com_Obody',
% 1.23/1.63 'tc_Com_Opname', 'tc_Com_Ocom' ), 'tc_Com_Opname' ) ] )
% 1.23/1.63 , clause( 1886, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, 'c_Com_Ocom_OSemi'( T, U ), W, Y
% 1.23/1.63 ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ) ), Y ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, U, W, Y ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 Y ), 'tc_bool' ) ) ), Y ) ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( X,
% 1.23/1.63 hAPP( hAPP( 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, T, V0, Y ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 Y ), 'tc_bool' ) ) ), Y ) ) ] )
% 1.23/1.63 , clause( 1887, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, 'c_Com_Ocom_OBODY'( T ), U, Y )
% 1.23/1.63 ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ) ), Y ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, 'c_Com_Ocom_OBODY'( T ), U, Y )
% 1.23/1.63 ), X ), hAPP( hAPP( 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( Y )
% 1.23/1.63 ), 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, 'c_Option_Othe'( hAPP(
% 1.23/1.63 'c_Com_Obody', T ), 'tc_Com_Ocom' ), U, Y ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 Y ), 'tc_bool' ) ) ), Y ) ) ] )
% 1.23/1.63 , clause( 1888, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, 'c_Com_Ocom_OBODY'( T ), U, Y )
% 1.23/1.63 ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ) ), Y ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, 'c_Option_Othe'( hAPP(
% 1.23/1.63 'c_Com_Obody', T ), 'tc_Com_Ocom' ), U, Y ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 Y ), 'tc_bool' ) ) ), Y ) ) ] )
% 1.23/1.63 , clause( 1889, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Z ), T ), Y ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( X, T, Y ) ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.63 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ) ), Y ) ) ] )
% 1.23/1.63 , clause( 1890, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP( 'c_Set_Oinsert'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( Z ) ), T ), Y ), Z ) ) ] )
% 1.23/1.63 , clause( 1891, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSKIP' ) ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1892, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ) ) ) ] )
% 1.23/1.63 , clause( 1893, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y
% 1.23/1.63 ), T ) ) ) ] )
% 1.23/1.63 , clause( 1894, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y
% 1.23/1.63 ), T ) ) ) ] )
% 1.23/1.63 , clause( 1895, [ hBOOL( hAPP( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ),
% 1.23/1.63 Y ) ) ] )
% 1.23/1.63 , clause( 1896, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( Y ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, 'c_Com_Ocom_OSKIP', Z, Y ) ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 Y ), 'tc_bool' ) ) ), Y ) ] )
% 1.23/1.63 , clause( 1897, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( X, T, Z ) ), ~(
% 1.23/1.63 'c_Hoare__Mirabelle_Ohoare__derivs'( T, Y, Z ) ) ] )
% 1.23/1.63 , clause( 1898, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.23/1.63 , clause( 1899, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.23/1.63 , Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1900, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.23/1.63 , clause( 1901, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.23/1.63 , clause( 1902, [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ) ) ) ] )
% 1.23/1.63 , clause( 1903, [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T )
% 1.23/1.63 , 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( Z, V0 ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1904, [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T )
% 1.23/1.63 , 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( Y, W ) ] )
% 1.23/1.63 , clause( 1905, [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T )
% 1.23/1.63 , 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( X, U ) ] )
% 1.23/1.63 , clause( 1906, [ =( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a'
% 1.23/1.63 , 'tc_bool' ) ), 'v_x' ), hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' ) ) ) ) ] )
% 1.23/1.63 , clause( 1907, [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ) ) ) ), =( Z, T ), =( Z, U ) ] )
% 1.23/1.63 , clause( 1908, [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ) ) ) ), =( Y, U ), =( Z, U ) ] )
% 1.23/1.63 , clause( 1909, [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ) ) ) ), =( Z, T ), =( Y, T ) ] )
% 1.23/1.63 , clause( 1910, [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), T ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ) ) ) ), =( Y, U ), =( Y, T ) ] )
% 1.23/1.63 , clause( 1911, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( Z )
% 1.23/1.63 , T ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( Z ), T ), Y ) )
% 1.23/1.63 ) ] )
% 1.23/1.63 , clause( 1912, [ hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP'
% 1.23/1.63 ), X ), X ) ) ] )
% 1.23/1.63 , clause( 1913, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), =( Y, T ),
% 1.23/1.63 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP( 'c_Set_Oinsert'( X )
% 1.23/1.63 , T ), Z ) ) ) ) ] )
% 1.23/1.63 , clause( 1914, [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.23/1.63 X, 'tc_bool' ) ), Y ) ) ) ] )
% 1.23/1.63 , clause( 1915, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X,
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 Y ), 'tc_bool' ) ), Y ) ] )
% 1.23/1.63 , clause( 1916, [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 hAPP( 'c_Set_Oinsert'( T ), Z ), X ), Y ) ) ) ] )
% 1.23/1.63 , clause( 1917, [ =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Y ), Z ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.23/1.63 Z ) ) ] )
% 1.23/1.63 , clause( 1918, [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ] )
% 1.23/1.63 , clause( 1919, [ ~( 'class_Orderings_Obot'( X ) ), =( hAPP(
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.23/1.63 , clause( 1920, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), hAPP(
% 1.23/1.63 hAPP( 'c_Set_Oinsert'( Z ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.23/1.63 Z, 'tc_bool' ) ) ) ) ) ) ] )
% 1.23/1.63 , clause( 1921, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Y ), Z ) ) ) ] )
% 1.23/1.63 , clause( 1922, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Y ), Z ) ) ) ] )
% 1.23/1.63 , clause( 1923, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Y ), Z ) ) ) ] )
% 1.23/1.63 , clause( 1924, [ =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Z ), T ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ),
% 1.23/1.63 hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), T ) ) ) ] )
% 1.23/1.63 , clause( 1925, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.23/1.63 hAPP( Z, Y ) ) ) ] )
% 1.23/1.63 , clause( 1926, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.23/1.63 , Y ), X ) ) ) ] )
% 1.23/1.63 , clause( 1927, [ =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Set_Oinsert'( X ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ) ) ) ] )
% 1.23/1.63 , clause( 1928, [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( X ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.63 'tc_bool' ) ) ) ) ), =( Y, Z ) ] )
% 1.23/1.63 , clause( 1929, [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.63 Z ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) )
% 1.23/1.63 ) ] )
% 1.23/1.63 , clause( 1930, [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL(
% 1.23/1.63 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ] )
% 1.23/1.63 , clause( 1931, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Z ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.23/1.63 Y ), 'tc_bool' ) ) ), Y ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( X,
% 1.23/1.63 hAPP( hAPP( 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Z ), T
% 1.23/1.63 ), Y ) ) ] )
% 1.23/1.63 , clause( 1932, [ hBOOL( hAPP( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ),
% 1.23/1.63 T ) ), ~( hBOOL( hAPP( Z, T ) ) ) ] )
% 1.23/1.63 , clause( 1933, [ ~( =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ), hAPP(
% 1.23/1.63 hAPP( 'c_Set_Oinsert'( X ), Y ), T ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X )
% 1.23/1.63 , Y ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), =( Z, T ) ] )
% 1.23/1.63 , clause( 1934, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OBODY'( Y ) )
% 1.23/1.63 ), =( X, Y ) ] )
% 1.23/1.63 , clause( 1935, [ =( hAPP( hAPP( 'c_Set_Oinsert'( X ), Y ), Z ), Z ), ~(
% 1.23/1.63 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.23/1.63 , clause( 1936, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OBODY'( X ) ) ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1937, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'(
% 1.23/1.63 'c_Com_Ocom_OSKIP' ), Y ), X ) ) ) ] )
% 1.23/1.63 , clause( 1938, [ ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'(
% 1.23/1.63 'c_Com_Ocom_OSKIP' ), 'v_x' ), 'v_x' ) ) ) ] )
% 1.23/1.63 , clause( 1939, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( 'v_G', hAPP( hAPP(
% 1.23/1.63 'c_Set_Oinsert'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ),
% 1.23/1.63 'c_Hoare__Mirabelle_Otriple_Otriple'( 'c_fequal'( 'tc_Com_Ostate' ),
% 1.23/1.63 'c_Com_Ocom_OBODY'( X ), 'c_Natural_Oevalc'( 'c_Com_Ocom_OBODY'( X ) ),
% 1.23/1.63 'tc_Com_Ostate' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.23/1.63 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) ) ),
% 1.23/1.63 'tc_Com_Ostate' ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_Com_Opname' ), X ),
% 1.23/1.63 'c_Map_Odom'( 'c_Com_Obody', 'tc_Com_Opname', 'tc_Com_Ocom' ) ) ) ) ] )
% 1.23/1.63 , clause( 1940, [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_fun'( X
% 1.23/1.63 , Y ) ), ~( 'class_Complete__Lattice_Ocomplete__lattice'( Y ) ) ] )
% 1.23/1.63 , clause( 1941, [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) )
% 1.23/1.63 , ~( 'class_Lattices_Olattice'( Y ) ) ] )
% 1.23/1.63 , clause( 1942, [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) )
% 1.23/1.63 , ~( 'class_Lattices_Olattice'( Y ) ) ] )
% 1.23/1.63 , clause( 1943, [ 'class_Lattices_Odistrib__lattice'( 'tc_fun'( X, Y ) ),
% 1.23/1.63 ~( 'class_Lattices_Odistrib__lattice'( Y ) ) ] )
% 1.23/1.63 , clause( 1944, [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ),
% 1.23/1.63 ~( 'class_Lattices_Obounded__lattice'( Y ) ) ] )
% 1.23/1.63 , clause( 1945, [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_fun'( X, Y ) ),
% 1.23/1.63 ~( 'class_Finite__Set_Ofinite_Ofinite'( Y ) ), ~(
% 1.23/1.63 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ] )
% 1.23/1.63 , clause( 1946, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.63 'class_Orderings_Opreorder'( Y ) ) ] )
% 1.23/1.63 , clause( 1947, [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.63 'class_Lattices_Olattice'( Y ) ) ] )
% 1.23/1.63 , clause( 1948, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.63 'class_Orderings_Oorder'( Y ) ) ] )
% 1.23/1.63 , clause( 1949, [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.63 'class_Orderings_Obot'( Y ) ) ] )
% 1.23/1.63 , clause( 1950, [ 'class_HOL_Ominus'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.63 'class_HOL_Ominus'( Y ) ) ] )
% 1.23/1.63 , clause( 1951, [ 'class_HOL_Oord'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Oord'(
% 1.23/1.63 Y ) ) ] )
% 1.23/1.63 , clause( 1952, [
% 1.23/1.63 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1953, [
% 1.23/1.63 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 1.23/1.63 )
% 1.23/1.63 , clause( 1954, [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.23/1.63 'tc_nat' ) ] )
% 1.23/1.63 , clause( 1955, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.23/1.63 'tc_nat' ) ] )
% 1.23/1.63 , clause( 1956, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.23/1.63 'tc_nat' ) ] )
% 1.23/1.63 , clause( 1957, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 1.23/1.63 'tc_nat' ) ] )
% 1.23/1.63 , clause( 1958, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 1.23/1.63 'tc_nat' ) ] )
% 1.23/1.63 , clause( 1959, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.23/1.63 'tc_nat' ) ] )
% 1.23/1.63 , clause( 1960, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 1.23/1.66 ] )
% 1.23/1.66 , clause( 1961, [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' )
% 1.23/1.66 ] )
% 1.23/1.66 , clause( 1962, [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ]
% 1.23/1.66 )
% 1.23/1.66 , clause( 1963, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 1.23/1.66 ] )
% 1.23/1.66 , clause( 1964, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 1.23/1.66 )
% 1.23/1.66 , clause( 1965, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ]
% 1.23/1.66 )
% 1.23/1.66 , clause( 1966, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 1.23/1.66 )
% 1.23/1.66 , clause( 1967, [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1968, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1969, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1970, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1971, [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1972, [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1973, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1974, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1975, [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1976, [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1977, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1978, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1979, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1980, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1981, [ 'class_Lattices_Olattice'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1982, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1983, [ 'class_Orderings_Obot'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1984, [ 'class_HOL_Ominus'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1985, [ 'class_HOL_Oord'( 'tc_nat' ) ] )
% 1.23/1.66 , clause( 1986, [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_bool' )
% 1.23/1.66 ] )
% 1.23/1.66 , clause( 1987, [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ] )
% 1.23/1.66 , clause( 1988, [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ] )
% 1.23/1.66 , clause( 1989, [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ] )
% 1.23/1.66 , clause( 1990, [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ] )
% 1.23/1.66 , clause( 1991, [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_bool' ) ] )
% 1.23/1.66 , clause( 1992, [ 'class_Orderings_Opreorder'( 'tc_bool' ) ] )
% 1.23/1.66 , clause( 1993, [ 'class_Lattices_Olattice'( 'tc_bool' ) ] )
% 1.23/1.66 , clause( 1994, [ 'class_Orderings_Oorder'( 'tc_bool' ) ] )
% 1.23/1.66 , clause( 1995, [ 'class_Orderings_Obot'( 'tc_bool' ) ] )
% 1.23/1.66 , clause( 1996, [ 'class_HOL_Ominus'( 'tc_bool' ) ] )
% 1.23/1.66 , clause( 1997, [ 'class_HOL_Oord'( 'tc_bool' ) ] )
% 1.23/1.66 , clause( 1998, [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_Option_Ooption'(
% 1.23/1.66 X ) ), ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ] )
% 1.23/1.66 , clause( 1999, [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ] )
% 1.23/1.66 , clause( 2000, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y
% 1.23/1.66 ) ) ) ] )
% 1.23/1.66 ] ).
% 1.23/1.66
% 1.23/1.66
% 1.23/1.66
% 1.23/1.66 subsumption(
% 1.23/1.66 clause( 872, [ hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP' )
% 1.23/1.66 , X ), X ) ) ] )
% 1.23/1.66 , clause( 1912, [ hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP'
% 1.23/1.66 ), X ), X ) ) ] )
% 1.23/1.66 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.23/1.66
% 1.23/1.66
% 1.23/1.66 resolution(
% 1.23/1.66 clause( 4232, [] )
% 1.23/1.66 , clause( 1938, [ ~( hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'(
% 1.23/1.66 'c_Com_Ocom_OSKIP' ), 'v_x' ), 'v_x' ) ) ) ] )
% 1.23/1.66 , 0, clause( 872, [ hBOOL( hAPP( hAPP( 'c_Natural_Oevalc'(
% 1.23/1.66 'c_Com_Ocom_OSKIP' ), X ), X ) ) ] )
% 1.23/1.66 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_x' )] )).
% 1.23/1.66
% 1.23/1.66
% 1.23/1.66 subsumption(
% 1.23/1.66 clause( 891, [] )
% 1.23/1.66 , clause( 4232, [] )
% 1.23/1.66 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.23/1.66
% 1.23/1.66
% 1.23/1.66 end.
% 1.23/1.66
% 1.23/1.66 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.23/1.66
% 1.23/1.66 Memory use:
% 1.23/1.66
% 1.23/1.66 space for terms: 84660
% 1.23/1.66 space for clauses: 91946
% 1.23/1.66
% 1.23/1.66
% 1.23/1.66 clauses generated: 1046
% 1.23/1.66 clauses kept: 892
% 1.23/1.66 clauses selected: 0
% 1.23/1.66 clauses deleted: 0
% 1.23/1.66 clauses inuse deleted: 0
% 1.23/1.66
% 1.23/1.66 subsentry: 19459
% 1.23/1.66 literals s-matched: 7849
% 1.23/1.66 literals matched: 7672
% 1.23/1.66 full subsumption: 3499
% 1.23/1.66
% 1.23/1.66 checksum: -12767427
% 1.23/1.66
% 1.23/1.66
% 1.23/1.66 Bliksem ended
%------------------------------------------------------------------------------