TSTP Solution File: SCT097-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SCT097-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.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 : Mon Jul 18 21:01:12 EDT 2022
% Result : Timeout 300.04s 300.51s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SCT097-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Fri Jul 1 22:36:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.23/1.61 *** allocated 10000 integers for termspace/termends
% 1.23/1.61 *** allocated 10000 integers for clauses
% 1.23/1.61 *** allocated 10000 integers for justifications
% 1.23/1.61 *** allocated 15000 integers for termspace/termends
% 1.23/1.61 *** allocated 22500 integers for termspace/termends
% 1.23/1.61 *** allocated 33750 integers for termspace/termends
% 1.23/1.61 *** allocated 50625 integers for termspace/termends
% 1.23/1.61 Bliksem 1.12
% 1.23/1.61
% 1.23/1.61
% 1.23/1.61 Automatic Strategy Selection
% 1.23/1.61
% 1.23/1.61 Clauses:
% 1.23/1.61 [
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.23/1.61 ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.23/1.61 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.23/1.61 ) ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( X ), Y, X ),
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.61 X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.23/1.61 ), X ) ],
% 1.23/1.61 [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.23/1.61 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.23/1.61 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.23/1.61 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.23/1.61 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.23/1.61 ), X ) ) ],
% 1.23/1.61 [ 'c_Relation_Osym'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 1.23/1.61 , 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Osym'(
% 1.23/1.61 Y, Z ) ), ~( 'c_Relation_Osym'( X, Z ) ) ],
% 1.23/1.61 [ =( 'c_Relation_ODomain'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, T ), U,
% 1.23/1.61 'tc_prod'( Z, T ) ), Z, T ), 'c_Set_Oinsert'( X, 'c_Relation_ODomain'( U
% 1.23/1.61 , Z, T ), Z ) ) ],
% 1.23/1.61 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.23/1.61 ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.23/1.61 , 'tc_bool' ) ) ],
% 1.23/1.61 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( 'c_Set_Oinsert'( Z,
% 1.23/1.61 X, T ), Y ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~(
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Z ), T ) ), W ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.23/1.61 ), W, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.23/1.61 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~(
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Z ), U ) ), W ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W
% 1.23/1.61 ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.23/1.61 Y, T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.23/1.61 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.23/1.61 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.23/1.61 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.23/1.61 'c_Set_Oinsert'( X, Y, Z ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ) ],
% 1.23/1.61 [ =( 'c_Relation_OImage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.23/1.61 , 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.23/1.61 , Z, X ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.23/1.61 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.23/1.61 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.23/1.61 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.23/1.61 , Z ), 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.61 'c_Set_Oinsert'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 1.23/1.61 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 1.23/1.61 'c_Set_Oinsert'( hAPP( Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.23/1.61 T, 'tc_bool' ) ), T ), X, T ) ) ) ],
% 1.23/1.61 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.23/1.61 ) ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.23/1.61 X, 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool'
% 1.23/1.61 ) ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( X ), Y, X ),
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( X ), X ), 'c_Orderings_Otop__class_Otop'(
% 1.23/1.61 X ) ) ],
% 1.23/1.61 [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ), Z, Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 1.23/1.61 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.23/1.61 ) ), Y, 'tc_fun'( X, 'tc_bool' ) ) ],
% 1.23/1.61 [ ~( =( hAPP( hAPP( 'c_Finite__Set_Osetsum'( X, 'tc_nat' ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z
% 1.23/1.61 , X ) ), =( hAPP( Y, T ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.23/1.61 hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Z ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ) ), U ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), T ), Z ) ), U ) ) ],
% 1.23/1.61 [ 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.23/1.61 'tc_bool' ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.23/1.61 'tc_bool' ) ), Z ), 'tc_fun'( X, 'tc_bool' ) ), ~( 'c_lessequals'( Z, Y,
% 1.23/1.61 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.23/1.61 hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Z, 'tc_bool' ) ), Y ),
% 1.23/1.61 hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Z, 'tc_bool' ) ), X ),
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.23/1.61 'tc_bool' ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.23/1.61 'tc_bool' ) ), Z ), 'tc_fun'( X, 'tc_bool' ) ), ~( 'c_lessequals'( Z, Y,
% 1.23/1.61 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_lessequals'( Z, Y, X
% 1.23/1.61 ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y,
% 1.23/1.61 X ), Z ), 'c_Lattices_Oupper__semilattice__class_Osup'( T, U, 'tc_fun'( Y
% 1.23/1.61 , 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( T, U, 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.61 hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.61 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'(
% 1.23/1.61 U, Y ) ), ~( 'c_Finite__Set_Ofinite'( T, Y ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Oone__class_Oone'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.23/1.61 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.23/1.61 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ),
% 1.23/1.61 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Set_Oinsert'( Y
% 1.23/1.61 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), T ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X, Y
% 1.23/1.61 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), Z ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.23/1.61 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.23/1.61 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.23/1.61 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 1.23/1.61 Y, Y ), 'tc_bool' ) ), Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~(
% 1.23/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.61 'c_lessequals'( Z, T, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~(
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.23/1.61 'c_lessequals'( T, Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.23/1.61 ) ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.61 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.23/1.61 ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.23/1.61 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.23/1.61 ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.23/1.61 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.61 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.23/1.61 ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.23/1.61 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.23/1.61 ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.23/1.61 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.23/1.61 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, X, Z ), 'tc_fun'( Z, 'tc_bool'
% 1.23/1.61 ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.23/1.61 'c_Power_Opower__class_Opower'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.23/1.61 , Y ), Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.61 'c_Power_Opower__class_Opower'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.23/1.61 , 'c_HOL_Oone__class_Oone'( X ) ), Z, X ) ),
% 1.23/1.61 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 1.23/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.23/1.61 ) ],
% 1.23/1.61 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'(
% 1.23/1.61 'c_Set_Oinsert'( Z, X, Y ), Y ) ) ],
% 1.23/1.61 [ 'c_Finite__Set_Ofinite'( 'c_Set_Oinsert'( X, Y, Z ), Z ), ~(
% 1.23/1.61 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.23/1.61 [ 'c_Finite__Set_Ofinite'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.61 'tc_bool' ) ), X ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.61 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.23/1.61 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~( hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ), T ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ), Z ) ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~( hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.61 Z ) ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ), T ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.23/1.61 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.23/1.61 ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.23/1.61 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.23/1.61 Z, X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 1.23/1.61 ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), T ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.23/1.61 ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 1.23/1.61 ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), T ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.23/1.61 ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y, hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), =( Y, Z ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.61 , Y ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.61 X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ), X ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.23/1.61 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( Y, Z )
% 1.23/1.61 ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ) ],
% 1.23/1.61 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( Y, Z )
% 1.23/1.61 ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( Y, Z,
% 1.23/1.61 X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.61 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ],
% 1.23/1.61 [ 'c_lessequals'( 'c_Relation_OImage'( X,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 1.23/1.61 'tc_fun'( U, 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ) ],
% 1.23/1.61 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ), 'c_lessequals'( T, X,
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( T, X,
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.23/1.61 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Finite__Set_Osetprod'( Y, Z, T
% 1.23/1.61 , X ), 'c_Finite__Set_Osetprod'( Y, U, T, X ), X ), ~( 'c_lessequals'( Z
% 1.23/1.61 , U, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.23/1.61 X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.61 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ), Y ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Y ) ) ), hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.61 Z ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.61 T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Y ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.61 ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.61 T ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.61 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.61 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.23/1.61 ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.61 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.23/1.61 ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.61 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), T ) ), Z ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.61 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.23/1.61 Y ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ) ],
% 1.23/1.61 [ 'c_lessequals'( 'c_Finite__Set_Ocard'( X, Y ), 'c_Finite__Set_Ocard'(
% 1.23/1.61 'c_Set_Oinsert'( Z, X, Y ), Y ), 'tc_nat' ), ~( 'c_Finite__Set_Ofinite'(
% 1.23/1.61 X, Y ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.23/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ),
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W
% 1.23/1.61 ) ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W
% 1.23/1.61 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), T ), U ) ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.23/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ),
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.23/1.61 ) ), W ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.23/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ) ), W ) ), ~(
% 1.23/1.61 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), T ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) )
% 1.23/1.61 ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ), ~( 'c_Finite__Set_Ofinite'( Y
% 1.23/1.61 , T ) ), =( hAPP( hAPP( 'c_Finite__Set_Osetsum'( T, X ), U ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_Finite__Set_Osetsum'( T, X ), U ), Y ) ), hAPP( hAPP(
% 1.23/1.61 'c_Finite__Set_Osetsum'( T, X ), U ), Z ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.61 ), Y ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( Y, T, X )
% 1.23/1.61 ), 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ) ],
% 1.23/1.61 [ 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.23/1.61 Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_lessequals'(
% 1.23/1.61 'c_Relation_Orel__comp'( X, Y, Z, Z, Z ), X, 'tc_fun'( 'tc_prod'( Z, Z )
% 1.23/1.61 , 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Y, Z ) ), ~(
% 1.23/1.61 'c_Wellfounded_Owf'( X, Z ) ) ],
% 1.23/1.61 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL( hAPP(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), Y ) ) ) ],
% 1.23/1.61 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ],
% 1.23/1.61 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 1.23/1.61 [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 'c_Relation_ODomain'( X, Y, Y ), 'c_Relation_ORange'( Z, Y, Y ), 'tc_fun'(
% 1.23/1.61 Y, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool'
% 1.23/1.61 ) ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ), ~( 'c_Wellfounded_Owf'( X, Y
% 1.23/1.61 ) ), 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ) ), =( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ) ), =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ],
% 1.23/1.61 [ 'c_Relation_Osingle__valued'( 'c_Relation_Orel__comp'( X, Y, Z, T, U )
% 1.23/1.61 , Z, U ), ~( 'c_Relation_Osingle__valued'( Y, T, U ) ), ~(
% 1.23/1.61 'c_Relation_Osingle__valued'( X, Z, T ) ) ],
% 1.23/1.61 [ 'c_Relation_Orefl__on'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 X, Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( T, U, 'tc_fun'( 'tc_prod'(
% 1.23/1.61 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Orefl__on'( Y, U, Z ) ), ~(
% 1.23/1.61 'c_Relation_Orefl__on'( X, T, Z ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Finite__Set_Ocard'(
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ), ~(
% 1.23/1.61 'c_Finite__Set_Ofinite'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.23/1.61 'tc_bool' ) ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.23/1.61 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.23/1.61 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.61 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.23/1.61 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.61 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.23/1.61 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.23/1.61 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ), Y ) ) ],
% 1.23/1.61 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ), Y ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( X ), Y, X ), Y ) ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.23/1.61 X, 'tc_bool' ) ), Y ) ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ), X ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 X ) ) ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.61 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.61 [ 'c_Relation_Orefl__on'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.23/1.61 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.61 'c_Relation_OId'( X ), 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' ) ), X ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.61 ],
% 1.23/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( X ) ) ), =( Z,
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( X ) ) ), =( Y,
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.61 , X ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.23/1.61 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.61 ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.23/1.61 ~( 'c_lessequals'( X, 'c_Relation_OImage'( Z, X, Y, Y ), 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Y,
% 1.23/1.61 'tc_fun'( X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.61 'tc_bool' ) ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), X ), 'tc_fun'(
% 1.23/1.61 Y, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool'
% 1.23/1.61 ) ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.23/1.61 Y ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.23/1.61 Y ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.23/1.61 Y ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.61 Y ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.61 Y ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.23/1.61 Y ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( 'c_lessequals'( Y, T, X
% 1.23/1.61 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ],
% 1.23/1.61 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.23/1.61 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1'( X, Z, T ) ) ) ),
% 1.23/1.61 ~( 'c_Wellfounded_Owf'( Z, T ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), U ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), U ) )
% 1.23/1.61 ), ~( 'c_lessequals'( Y, T, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.61 ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.61 'c_Power_Opower__class_Opower'( Y, Z, X ) ),
% 1.23/1.61 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.23/1.61 ), Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.61 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.23/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), hAPP(
% 1.23/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.61 hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), hAPP(
% 1.23/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ), X ), ~( 'c_lessequals'( Y
% 1.23/1.61 , Z, 'tc_nat' ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Z,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.23/1.61 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.61 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.61 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.23/1.61 ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.61 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.23/1.61 ) ) ],
% 1.23/1.61 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.23/1.61 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_Set_Oinsert'( T, X, Z ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.23/1.61 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.61 ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.61 X ), Y ), Z ) ), Z ), Y ) ],
% 1.23/1.61 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), 'c_Set_Oinsert'( Y
% 1.23/1.61 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.23/1.61 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 1.23/1.61 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.61 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X, 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ), X ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ],
% 1.23/1.61 [ 'c_lessequals'( 'c_Relation_Orel__comp'( X, Y, Z, T, U ),
% 1.23/1.61 'c_Relation_Orel__comp'( W, V0, Z, T, U ), 'tc_fun'( 'tc_prod'( Z, U ),
% 1.23/1.61 'tc_bool' ) ), ~( 'c_lessequals'( Y, V0, 'tc_fun'( 'tc_prod'( T, U ),
% 1.23/1.61 'tc_bool' ) ) ), ~( 'c_lessequals'( X, W, 'tc_fun'( 'tc_prod'( Z, T ),
% 1.23/1.61 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.23/1.61 'c_HOL_Osgn__class_Osgn'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.61 ), 'c_HOL_Oone__class_Oone'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.61 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.61 X ), Y ), Z ) ), T ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.61 X ), Y ), Z ) ), T ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.23/1.61 [ =( 'c_Relation_OImage'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 X, Y, 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ), U, Z, T ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_OImage'( X, U,
% 1.23/1.61 Z, T ), 'c_Relation_OImage'( Y, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ =( 'c_Relation_OImage'( X,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), T, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 1.23/1.61 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.61 ), Y ) ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.23/1.61 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.23/1.61 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1'( X, Z, T ) ) ) ), ~(
% 1.23/1.61 'c_Wellfounded_Owf'( Z, T ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.61 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.23/1.61 [ 'c_lessequals'( 'c_Relation_OImage'( X, Y, Z, T ), U, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), ~( 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), 'c_Relation_OImage'( 'c_Relation_Oconverse'(
% 1.23/1.61 X, Z, T ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( T, 'tc_bool' )
% 1.23/1.61 ), U ), T, Z ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ 'c_lessequals'( X, hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ), 'c_Relation_OImage'( 'c_Relation_Oconverse'( Z, Y, T ),
% 1.23/1.61 hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( T, 'tc_bool' ) ), U ), T
% 1.23/1.61 , Y ) ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_Relation_OImage'( Z, X, Y, T ), U, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 1.23/1.61 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.23/1.61 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.23/1.61 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.61 [ 'c_Relation_Osingle__valued'( 'c_Relation_OId'( X ), X, X ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.23/1.61 Y, T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.23/1.61 ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 1.23/1.61 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 'tc_nat' ) ), 'c_Finite__Set_Ocard'( X, Y ) ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.23/1.61 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.23/1.61 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.61 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.23/1.61 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.61 ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.23/1.61 'c_lessequals'( T, Z, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.61 ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.23/1.61 ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.23/1.61 'c_lessequals'( Z, T, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.61 ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.61 'c_lessequals'( Y, Z, X ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.23/1.61 ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T )
% 1.23/1.61 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.61 'c_lessequals'( Y, Z, X ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.23/1.61 ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.23/1.61 , T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.23/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.61 , Y ), T ), Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.23/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.61 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.23/1.61 ), X ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.61 ), T ), Z ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.23/1.61 Y, X ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.61 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ =( X, Y ), ~( 'c_lessequals'( 'c_Finite__Set_Ocard'( Y, Z ),
% 1.23/1.61 'c_Finite__Set_Ocard'( X, Z ), 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_Orderings_Otop__class_Otop'( X )
% 1.23/1.61 ), 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.23/1.61 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.61 ) ), Z ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.61 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.23/1.61 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.23/1.61 ) ), Y ) ) ) ],
% 1.23/1.61 [ ~( =( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.23/1.61 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_in'( X ), Y ), T ) ) ), ~( =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, 'tc_fun'( X,
% 1.23/1.61 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.61 ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( X ), X ), Y ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( X ), Y, X ), Y ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.23/1.61 X, 'tc_bool' ) ), Y ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ), X ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), X ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.23/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.61 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Y ) ],
% 1.23/1.61 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.23/1.61 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1'( X, Z, T ) ) ) ), ~(
% 1.23/1.61 'c_Wellfounded_Owf'( Z, T ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ), Z ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.61 [ hBOOL( hAPP( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' )
% 1.23/1.61 ), Y ) ) ],
% 1.23/1.61 [ =( 'c_Finite__Set_Ocard'( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.23/1.61 ) ), 'c_Finite__Set_Ofinite'( X, Y ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.23/1.61 [ ~( =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.61 , Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.23/1.61 Z ) ) ), =( Y, Z ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.61 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.23/1.61 T, X ) ), 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.61 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.23/1.61 ],
% 1.23/1.61 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_Wellfounded_Oacyclic'(
% 1.23/1.61 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 1.23/1.61 [ 'c_Wellfounded_Oacyclic'( 'c_Relation_Oconverse'( X, Y, Y ), Y ), ~(
% 1.23/1.61 'c_Wellfounded_Oacyclic'( X, Y ) ) ],
% 1.23/1.61 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.23/1.61 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.23/1.61 , Y, 'tc_nat' ) ) ],
% 1.23/1.61 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.23/1.61 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.23/1.61 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.23/1.61 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.23/1.61 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetprod'( Y,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( U,
% 1.23/1.61 'tc_bool' ) ), U, X ) ), 'c_Finite__Set_Osetprod'( Y,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( U,
% 1.23/1.61 'tc_bool' ) ), U, X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.61 'c_Finite__Set_Osetprod'( Y, Z, U, X ) ), 'c_Finite__Set_Osetprod'( Y, T
% 1.23/1.61 , U, X ) ) ), ~( 'c_Finite__Set_Ofinite'( T, U ) ), ~(
% 1.23/1.61 'c_Finite__Set_Ofinite'( Z, U ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), ~( =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) )
% 1.23/1.61 ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ), ~( 'c_Finite__Set_Ofinite'( Y
% 1.23/1.61 , T ) ), =( 'c_Finite__Set_Osetprod'( U,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), T, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.61 'c_Finite__Set_Osetprod'( U, Y, T, X ) ), 'c_Finite__Set_Osetprod'( U, Z
% 1.23/1.61 , T, X ) ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ), Y ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~(
% 1.23/1.61 'c_lessequals'( Z, Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ),
% 1.23/1.61 'c_lessequals'( Y, Z, X ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~(
% 1.23/1.61 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), Y ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) )
% 1.23/1.61 ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), X ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) )
% 1.23/1.61 ],
% 1.23/1.61 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.23/1.61 , 'tc_bool' ) ), Y ) ), 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) )
% 1.23/1.61 ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.61 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.61 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z
% 1.23/1.61 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ), X ), ~( 'c_lessequals'( U
% 1.23/1.61 , Z, X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), U ) ) ), ~( 'c_lessequals'( Y, T, X )
% 1.23/1.61 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_Finite__Set_Osetsum'( Y, X ), Z ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( T, U, 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.61 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ) ), hAPP( hAPP(
% 1.23/1.61 'c_Finite__Set_Osetsum'( Y, X ), Z ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( T, U, 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ) ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ), ~(
% 1.23/1.61 'c_Finite__Set_Ofinite'( T, Y ) ) ],
% 1.23/1.61 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.23/1.61 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ],
% 1.23/1.61 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.23/1.61 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ],
% 1.23/1.61 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.23/1.61 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ],
% 1.23/1.61 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.23/1.61 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), X ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), Z ), X ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.61 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.23/1.61 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.61 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.61 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.23/1.61 'c_lessequals'( Z, T, X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.61 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.23/1.61 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.23/1.61 'c_lessequals'( Z, T, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.61 X ), Y ) ), Z ) ) ],
% 1.23/1.61 [ =( 'c_Finite__Set_Ocard'( 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.23/1.61 'c_Finite__Set_Ocard'( Y, Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ),
% 1.23/1.61 Y ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.23/1.61 [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.23/1.61 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.23/1.61 'tc_bool' ) ), ~( 'c_lessequals'( X, 'c_Transitive__Closure_Ortrancl'( Z
% 1.23/1.61 , Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.23/1.61 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 1.23/1.61 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T )
% 1.23/1.61 ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.61 Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) )
% 1.23/1.61 ) ],
% 1.23/1.61 [ 'c_Finite__Set_Ofinite'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.23/1.61 'tc_bool' ) ), X ), ~( 'c_Finite__Set_Ofinite'( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), X ) ),
% 1.23/1.61 ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.23/1.61 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.61 'tc_fun'( X, 'tc_bool' ) ), Y ), X ), ~( 'c_Finite__Set_Ofinite'(
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X ) ), ~(
% 1.23/1.61 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.23/1.61 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.23/1.61 ~( 'c_lessequals'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.23/1.61 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.23/1.61 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.23/1.61 ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.23/1.61 'tc_fun'( X, 'tc_bool' ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.23/1.61 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.23/1.61 'c_Set_Oinsert'( Y, Z, X ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.23/1.61 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.61 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.61 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.23/1.61 'c_lessequals'( Z, U, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.61 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ),
% 1.23/1.61 ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.23/1.61 X ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.23/1.61 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Set_Oinsert'( Y
% 1.23/1.61 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), X ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) )
% 1.23/1.61 ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) )
% 1.23/1.61 ],
% 1.23/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~(
% 1.23/1.61 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ),
% 1.23/1.61 'c_lessequals'( Y, Z, X ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~(
% 1.23/1.61 'c_lessequals'( Z, Y, X ) ) ],
% 1.23/1.61 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.23/1.61 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.23/1.61 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X
% 1.23/1.61 , 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.23/1.61 [ 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 1.23/1.61 , 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.23/1.61 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.23/1.61 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.23/1.61 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.23/1.61 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.23/1.61 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.23/1.61 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, X,
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.23/1.61 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_Wellfounded_Owf'( X, Y ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ 'c_lessequals'( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.23/1.61 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z
% 1.23/1.61 ) ), 'c_Pair'( Y, T, Z, Z ) ), X ) ) ), ~( 'c_Equiv__Relations_Oequiv'(
% 1.23/1.61 U, X, Z ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.23/1.61 ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), X ) ],
% 1.23/1.61 [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.23/1.61 'c_Transitive__Closure_Ortrancl'( Z, Y ) ), ~( 'c_lessequals'( X,
% 1.23/1.61 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.23/1.61 'tc_bool' ) ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.23/1.61 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.61 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.61 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.61 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( X ) ) ), ~( =(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( X ) ) ), =( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ],
% 1.23/1.61 [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.23/1.61 , 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 1.23/1.61 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X, Z ) ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( T, X, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.23/1.61 , X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.23/1.61 Z, X ) ), 'c_Power_Opower__class_Opower'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 'tc_nat' ) ), Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.61 , Y, X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T
% 1.23/1.61 ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.61 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 X ) ) ), =( Y, Z ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.61 X ) ) ), =( Y, Z ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.23/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.61 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.23/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Y,
% 1.23/1.61 'tc_fun'( X, 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.23/1.61 'tc_bool' ) ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), X ), 'tc_fun'(
% 1.23/1.61 Y, 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool'
% 1.23/1.61 ) ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.61 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.61 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), Y )
% 1.23/1.61 ) ],
% 1.23/1.61 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.23/1.61 ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ), Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.23/1.61 ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.61 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~(
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.61 Y ) ) ) ],
% 1.23/1.61 [ =( 'c_Set_Ovimage'( X, hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'(
% 1.23/1.61 Y, 'tc_bool' ) ), Z ), T, Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.61 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Ovimage'( X, Z, T, Y ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.23/1.61 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.23/1.61 'c_Set_Oinsert'( Y, T, X ), Z, 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ =( 'c_Product__Type_OSigma'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), T, Z, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 'c_Product__Type_OSigma'( X, T, Z, U ), 'c_Product__Type_OSigma'( Y, T, Z
% 1.23/1.61 , U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ],
% 1.23/1.61 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL( hAPP( Y, T )
% 1.23/1.61 ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.61 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.23/1.61 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.23/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.23/1.61 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.23/1.61 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_in'( T ), Y ), X ) ) ],
% 1.23/1.61 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_in'( Z ), T ), X ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( T, Y, Z )
% 1.23/1.61 , 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.23/1.61 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_in'( T ), Y ), X ) ) ],
% 1.23/1.61 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 1.23/1.61 , 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.23/1.61 hAPP( 'c_in'( Z ), T ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.23/1.61 ,
% 1.23/1.61 [ 'c_lessequals'( 'c_Set_Ovimage'( X, Y, Z, T ), 'c_Set_Ovimage'( X, U,
% 1.23/1.61 Z, T ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, U, 'tc_fun'( T
% 1.23/1.61 , 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.61 ), Y ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Set_Oinsert'( Y
% 1.23/1.61 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.23/1.61 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ],
% 1.23/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.23/1.61 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.23/1.61 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.23/1.61 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.23/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.61 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.61 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.61 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.23/1.61 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.23/1.61 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.23/1.61 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.23/1.61 ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.23/1.61 ) ],
% 1.23/1.61 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.23/1.61 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.23/1.61 ) ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.23/1.61 ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 1.23/1.61 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.23/1.61 [ ~( =( 'c_Finite__Set_Ocard'( X, Y ), 'c_Finite__Set_Ocard'(
% 1.23/1.61 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), ~(
% 1.23/1.61 'c_Finite__Set_Ofinite'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ), Y ) ), =( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.23/1.61 'tc_bool' ) ) ) ],
% 1.23/1.61 [ =( 'c_Relation_Orel__comp'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 1.23/1.61 Z, T ), 'tc_bool' ) ), U, Z, T, W ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 1.23/1.61 , U, Z, T, W ), 'c_Relation_Orel__comp'( Y, U, Z, T, W ), 'tc_fun'(
% 1.23/1.61 'tc_prod'( Z, W ), 'tc_bool' ) ) ) ],
% 1.23/1.61 [ =( 'c_Relation_Orel__comp'( X,
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 'tc_prod'(
% 1.23/1.61 T, U ), 'tc_bool' ) ), W, T, U ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 1.23/1.61 , Y, W, T, U ), 'c_Relation_Orel__comp'( X, Z, W, T, U ), 'tc_fun'(
% 1.23/1.61 'tc_prod'( W, U ), 'tc_bool' ) ) ) ],
% 1.23/1.61 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 1.23/1.61 , 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 1.23/1.61 , 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.23/1.61 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.23/1.61 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 Z, T, X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.23/1.61 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 T, Z, X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 1.23/1.61 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 1.23/1.61 'c_lessequals'( Z, T, X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.23/1.61 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 Z, T, X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.23/1.61 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.61 T, Z, X ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.61 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP(
% 1.23/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) ) ],
% 1.23/1.61 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 1.23/1.61 ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.23/1.61 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.61 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.61 [ 'c_Relation_Ototal__on'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.61 'tc_bool' ) ), Y, X ) ],
% 1.23/1.61 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.23/1.61 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.61 T, U, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.23/1.61 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.23/1.61 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.61 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ),
% 1.23/1.61 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 1.23/1.61 'tc_fun'( U, 'tc_bool' ) ), U ), T, U ) ) ) ) ],
% 1.23/1.61 [ =( 'c_Relation_Oconverse'(
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 1.23/1.61 Z, T ), 'tc_bool' ) ), Z, T ),
% 1.23/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Oconverse'( X,
% 1.23/1.61 Z, T ), 'c_Relation_Oconverse'( Y, Z, T ), 'tc_fun'( 'tc_prod'( T, Z ),
% 1.23/1.61 'tc_bool' ) ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.23/1.61 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.61 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.61 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.61 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.23/1.61 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.23/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.23/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 1.23/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 1.23/1.62 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.23/1.62 'tc_fun'( Z, 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.23/1.62 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.23/1.62 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z
% 1.23/1.62 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 1.23/1.62 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.23/1.62 , Y, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z
% 1.23/1.62 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 1.23/1.62 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.23/1.62 , Y, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.23/1.62 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Otop'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_Orderings_Otop__class_Otop'( X ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Osgn__class_Osgn'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.62 ), 'c_HOL_Oone__class_Oone'( X ) ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.23/1.62 'c_HOL_Osgn__class_Osgn'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.62 ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.23/1.62 , Z, X ), 'c_Power_Opower__class_Opower'( T, U, X ), X ), ~(
% 1.23/1.62 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.23/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.62 ), Y ) ), Z ) ), Z ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.23/1.62 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.23/1.62 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( T,
% 1.23/1.62 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z,
% 1.23/1.62 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.23/1.62 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 1.23/1.62 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.23/1.62 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ],
% 1.23/1.62 [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool'
% 1.23/1.62 ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_Orderings_Obot__class_Obot'( X )
% 1.23/1.62 ), 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.23/1.62 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.23/1.62 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.23/1.62 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.23/1.62 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.23/1.62 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ =( 'c_Relation_OImage'( X,
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.23/1.62 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.62 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 1.23/1.62 'tc_fun'( U, 'tc_bool' ) ) ), ~( 'c_Relation_Osingle__valued'(
% 1.23/1.62 'c_Relation_Oconverse'( X, T, U ), U, T ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.23/1.62 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.23/1.62 T, X ) ), 'c_Power_Opower__class_Opower'( Z, T, X ) ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.23/1.62 Z, X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.23/1.62 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), Y ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.62 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ), 'c_Finite__Set_Ofinite'(
% 1.23/1.62 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ =( 'c_Relation_ORange'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.62 X, Y, 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ), Z, T ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_ORange'( X, Z,
% 1.23/1.62 T ), 'c_Relation_ORange'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.23/1.62 , ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.23/1.62 , Y ), T ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ],
% 1.23/1.62 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X, 'tc_fun'( Y,
% 1.23/1.62 'tc_bool' ) ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), T ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.23/1.62 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 1.23/1.62 Y, X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.23/1.62 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.62 T, X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.23/1.62 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 1.23/1.62 Y, X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.23/1.62 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.62 T, X ), Z, X ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 1.23/1.62 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 1.23/1.62 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 1.23/1.62 Y, Z, X ), X ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.23/1.62 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.23/1.62 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.23/1.62 , Z, X ), T, X ), ~( 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.23/1.62 , U, X ), T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.23/1.62 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.23/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.23/1.62 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.23/1.62 [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( T
% 1.23/1.62 , Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 1.23/1.62 'tc_bool' ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( Z, Y ) ) ), ~( 'c_lessequals'(
% 1.23/1.62 Z, X, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_lessequals'( X, Z, 'tc_fun'(
% 1.23/1.62 'tc_prod'( Y, Y ), 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.23/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), T ) ), =( T,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), Z ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ) ],
% 1.23/1.62 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.23/1.62 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X,
% 1.23/1.62 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.23/1.62 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.23/1.62 X, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ) ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ) ) ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.62 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.23/1.62 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.23/1.62 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.23/1.62 T, Z, X ) ) ), =( Y, T ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ =( 'c_Relation_ODomain'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.62 X, Y, 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ), Z, T ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_ODomain'( X, Z
% 1.23/1.62 , T ), 'c_Relation_ODomain'( Y, Z, T ), 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y, hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), T ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y,
% 1.23/1.62 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.23/1.62 [ 'c_lessequals'( 'c_Wellfounded_Oacc'( X, Y ), 'c_Wellfounded_Oacc'( Z
% 1.23/1.62 , Y ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'(
% 1.23/1.62 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 1.23/1.62 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.23/1.62 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.23/1.62 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.23/1.62 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.23/1.62 X, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.23/1.62 [ 'c_lessequals'( 'c_Finite__Set_Ocard'( X, Y ), 'c_Finite__Set_Ocard'(
% 1.23/1.62 Z, Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) )
% 1.23/1.62 , ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.23/1.62 [ =( 'c_Set_Ovimage'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y
% 1.23/1.62 , Z, 'tc_fun'( T, 'tc_bool' ) ), U, T ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Ovimage'( X, Y, U, T
% 1.23/1.62 ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Power_Opower__class_Opower'( Y
% 1.23/1.62 , Z, X ) ) ), 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Finite__Set_Ocard'(
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1'( X, Z, T ) ) )
% 1.23/1.62 ), ~( 'c_Wellfounded_Owf'( Z, T ) ) ],
% 1.23/1.62 [ =( 'c_Transitive__Closure_Ortrancl'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.23/1.62 'tc_bool' ) ), Y ), 'c_Transitive__Closure_Ortrancl'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 1.23/1.62 Y, Y ), 'tc_bool' ) ), Y ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), T ) ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), T ) ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Y ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Y ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.23/1.62 [ =( 'c_Finite__Set_Ocard'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X
% 1.23/1.62 , 'tc_bool' ) ), X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.23/1.62 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Osgn__class_Osgn'( Y, X ), X ),
% 1.23/1.62 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Finite__Set_Ocard'( X, Y ) )
% 1.23/1.62 ), ~( 'c_Finite__Set_Ofinite'( X, Y ) ), =( X,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.23/1.62 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.23/1.62 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 1.23/1.62 'tc_bool' ) ), Y ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.23/1.62 'tc_bool' ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.23/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.23/1.62 [ =( 'c_Relation_ORange'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, T ), U,
% 1.23/1.62 'tc_prod'( Z, T ) ), Z, T ), 'c_Set_Oinsert'( Y, 'c_Relation_ORange'( U,
% 1.23/1.62 Z, T ), T ) ) ],
% 1.23/1.62 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.23/1.62 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.23/1.62 ), ~( 'c_lessequals'( X, hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'(
% 1.23/1.62 Z, 'tc_bool' ) ), Y ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z
% 1.23/1.62 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.23/1.62 ) ) ), 'c_lessequals'( X, hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'(
% 1.23/1.62 Z, 'tc_bool' ) ), Y ), 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.62 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.23/1.62 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( 'c_lessequals'( Y, hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.23/1.62 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), T ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Z ), Y ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Z ), Y ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), Z ), Y ) ],
% 1.23/1.62 [ ~( =( hAPP( X, 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X, Y, Z, T, U,
% 1.23/1.62 W ) ), hAPP( Y, 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X, Y, Z, T, U, W
% 1.23/1.62 ) ) ) ), =( 'c_Recdef_Ocut'( X, Z, T, U, W ), 'c_Recdef_Ocut'( Y, Z, T,
% 1.23/1.62 U, W ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.62 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 1.23/1.62 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), T
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.62 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 1.23/1.62 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), T
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.23/1.62 Y, T, X ), X ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ 'c_Relation_Osingle__valued'( 'c_Relation_OId__on'( X, Y ), Y, Y ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.23/1.62 hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ) ),
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 X ), Y ) ), Y ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 X ), Y ) ), Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 X ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 X ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 X ), Y ) ), Y ) ],
% 1.23/1.62 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_Wellfounded_Oacyclic'(
% 1.23/1.62 'c_Set_Oinsert'( 'c_Pair'( Z, T, Y, Y ), X, 'tc_prod'( Y, Y ) ), Y ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'( Z, Y ) ), ~(
% 1.23/1.62 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 1.23/1.62 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) )
% 1.23/1.62 , ~( 'c_lessequals'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( T, 'tc_bool'
% 1.23/1.62 ) ) ), ~( hBOOL( hAPP( Z, Y ) ) ) ],
% 1.23/1.62 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_lessequals'( X, Z, 'tc_fun'(
% 1.23/1.62 'tc_prod'( Y, Y ), 'tc_bool' ) ) ), ~( 'c_Wellfounded_Oacyclic'( Z, Y ) )
% 1.23/1.62 ],
% 1.23/1.62 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_lessequals'( X, Z, 'tc_fun'( Y
% 1.23/1.62 , 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ],
% 1.23/1.62 [ 'c_Relation_Osingle__valued'( X, Y, Z ), ~(
% 1.23/1.62 'c_Relation_Osingle__valued'( T, Y, Z ) ), ~( 'c_lessequals'( X, T,
% 1.23/1.62 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.23/1.62 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.23/1.62 [ ~( =( 'c_Finite__Set_Ocard'( X, Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 'tc_nat' ) ) ), ~( 'c_Finite__Set_Ofinite'( X, Y ) ), =( X,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.23/1.62 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.62 T, U, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.23/1.62 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.23/1.62 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.62 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.23/1.62 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.23/1.62 ~( 'c_lessequals'( X, hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y,
% 1.23/1.62 'tc_bool' ) ), X ), 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ 'c_lessequals'( 'c_Relation_ODomain'( X, Y, Z ), 'c_Relation_ODomain'(
% 1.23/1.62 T, Y, Z ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'( X, T, 'tc_fun'(
% 1.23/1.62 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ],
% 1.23/1.62 [ =( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 1.23/1.62 , 'tc_bool' ) ), Z ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 1.23/1.62 , 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.23/1.62 Z, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ =( 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Y, Z, T ), U, T ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Ovimage'( X,
% 1.23/1.62 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.23/1.62 'tc_bool' ) ), T ), U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U,
% 1.23/1.62 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.23/1.62 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( X, T ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( U, T, X
% 1.23/1.62 ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( Z, Y, X
% 1.23/1.62 ), ~( 'c_lessequals'( U, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.23/1.62 'c_Power_Opower__class_Opower'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Power_Opower__class_Opower'( Y, T, X ) ),
% 1.23/1.62 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.23/1.62 'c_Power_Opower__class_Opower'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Power_Opower__class_Opower'( Y, T, X ) ),
% 1.23/1.62 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ],
% 1.23/1.62 [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z )
% 1.23/1.62 , 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z,
% 1.23/1.62 'tc_bool' ) ) ) ],
% 1.23/1.62 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.62 X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), W ) ) ), T
% 1.23/1.62 ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.62 X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), W
% 1.23/1.62 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), W ), X ) ), ~(
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), U ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), =( U,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z
% 1.23/1.62 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.23/1.62 'c_HOL_Osgn__class_Osgn'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_HOL_Osgn__class_Osgn'( Y, X ) ), 'c_HOL_Osgn__class_Osgn'( Z, X ) ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.23/1.62 'tc_bool' ) ), Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.23/1.62 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.23/1.62 [ 'c_lessequals'( 'c_Relation_OImage'( X, Y, Z, T ), 'c_Relation_OImage'(
% 1.23/1.62 U, W, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y, W,
% 1.23/1.62 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, U, 'tc_fun'(
% 1.23/1.62 'tc_prod'( Z, T ), 'tc_bool' ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.62 ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.62 ), Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), ~( 'c_lessequals'( U
% 1.23/1.62 , Z, X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.23/1.62 'c_lessequals'( Z, Y, X ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( X, Y ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( Z ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 'tc_nat' ) ), 'c_Finite__Set_Osetprod'( X, T, Z, 'tc_nat' ) ) ) ), ~(
% 1.23/1.62 'c_Finite__Set_Ofinite'( T, Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.62 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 'tc_nat' ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X
% 1.23/1.62 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), Z ), 'c_Set_Oinsert'( T, U, Y ) ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Z, T ) ), hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.62 Y ), T ), U ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, 'c_Set_Oinsert'( Z, T, U ), U, X ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, Z ) ),
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, T, U, X ) ) ), hBOOL( hAPP( hAPP( 'c_in'( U
% 1.23/1.62 ), Z ), T ) ), ~( 'c_Finite__Set_Ofinite'( T, U ) ) ],
% 1.23/1.62 [ 'c_Wellfounded_Oacyclic'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, Z ), T,
% 1.23/1.62 'tc_prod'( Z, Z ) ), Z ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) )
% 1.23/1.62 , 'c_Pair'( Y, X, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( T, Z ) ) )
% 1.23/1.62 , ~( 'c_Wellfounded_Oacyclic'( T, Z ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X,
% 1.23/1.62 X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~(
% 1.23/1.62 'c_Wellfounded_Oacyclic'( 'c_Set_Oinsert'( 'c_Pair'( Z, Y, X, X ), T,
% 1.23/1.62 'tc_prod'( X, X ) ), X ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) )
% 1.23/1.62 , 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'(
% 1.23/1.62 X, T, U, Z ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 1.23/1.62 X, T, U, Z ), Z, Z ) ), U ) ), ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) )
% 1.23/1.62 , 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, T,
% 1.23/1.62 U, Z ), 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2'(
% 1.23/1.62 X, T, U, Z ), Z, Z ) ), U ) ), ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( T, Y, Z, Z ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_OImage'( Z,
% 1.23/1.62 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ), X ), X, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T
% 1.23/1.62 ) ) ), ~( 'c_Equiv__Relations_Oequiv'( T, Z, X ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), U ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Relation_OImage'( T,
% 1.23/1.62 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ), X ), X, X ), 'c_Relation_OImage'( T, 'c_Set_Oinsert'( Z,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X, X ),
% 1.23/1.62 'tc_fun'( X, 'tc_bool' ) ) ) ) ), ~( 'c_Equiv__Relations_Oequiv'( W, T, X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), U ) ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_Relation_OImage'( T, 'c_Set_Oinsert'( Z,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X, X ),
% 1.23/1.62 'c_Relation_OImage'( T, 'c_Set_Oinsert'( Y,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X, X ),
% 1.23/1.62 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, T, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.62 X ), Y ), Y ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 T ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), T ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.23/1.62 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), T ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.23/1.62 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Z ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( 'c_lessequals'( Y, T, X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( 'c_lessequals'( Z, U, X
% 1.23/1.62 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) )
% 1.23/1.62 ],
% 1.23/1.62 [ =( 'c_Set_Ovimage'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y
% 1.23/1.62 , Z, 'tc_fun'( T, 'tc_bool' ) ), U, T ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Ovimage'( X, Y, U, T
% 1.23/1.62 ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.62 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( Y, Z )
% 1.23/1.62 ) ],
% 1.23/1.62 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.23/1.62 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( hAPP( Y, Z ), hAPP( T, Z )
% 1.23/1.62 , X ), ~( 'c_lessequals'( Y, T, 'tc_fun'( U, X ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.23/1.62 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.23/1.62 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.23/1.62 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.23/1.62 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T, X ) ) ),
% 1.23/1.62 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T, X ) ) ),
% 1.23/1.62 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( 'c_lessequals'( T, Z,
% 1.23/1.62 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T )
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.62 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.62 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.62 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), =( Y, T ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( T, Z, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.62 X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( T, Z, 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Otop__class_Otop'(
% 1.23/1.62 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Z ) ) ),
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ), Z ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( X ), Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z,
% 1.23/1.62 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( X ), Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T,
% 1.23/1.62 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.23/1.62 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z ) ) ),
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( Z
% 1.23/1.62 ), X ), Y ) ), =( Y, T ) ],
% 1.23/1.62 [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.23/1.62 , X ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( Y, Z, X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.23/1.62 , Z, X ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( Y, Z, X )
% 1.23/1.62 ), =( Y, Z ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.23/1.62 Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.23/1.62 Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( Y, Z, X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( Y, Z, X )
% 1.23/1.62 ), =( Z, Y ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Z, Y ), ~( 'c_lessequals'(
% 1.23/1.62 Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), T ), U ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), T ), U ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( T, Z, X )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( 'c_lessequals'( Y, T, X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( Y, T, X )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ) ), ~(
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ) ), ~(
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), 'c_lessequals'( Z, Y, X ),
% 1.23/1.62 ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.23/1.62 , Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), 'c_lessequals'( Z, Y, X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( 'c_lessequals'( Z, Y, X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ],
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), 'c_lessequals'( Z, Y, X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), T ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Z ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 X ), Y ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 X ), Y ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.23/1.62 , Z ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.23/1.62 , Z ) ), Y ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.23/1.62 =( X, Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ =( X, Y ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X
% 1.23/1.62 ), Y ) ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.23/1.62 =( X, Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 'tc_nat' ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), =( X,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.23/1.62 [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.23/1.62 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.23/1.62 ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z
% 1.23/1.62 ) ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ) ), ~(
% 1.23/1.62 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ],
% 1.23/1.62 [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.23/1.62 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.23/1.62 ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z ) ), X ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( Z ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.23/1.62 , Y ), U ) ) ) ],
% 1.23/1.62 [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.23/1.62 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z
% 1.23/1.62 ) ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( Z ), Y ), U ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U
% 1.23/1.62 , X, Z ) ) ],
% 1.23/1.62 [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.23/1.62 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( Z ), Y ), U ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ),
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z ) )
% 1.23/1.62 , X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBS'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y, 'tc_bool'
% 1.23/1.62 ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T
% 1.23/1.62 , Y, X, 'tc_fun'( X, X ) ), U, Y, X, X ) ), W ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y,
% 1.23/1.62 X ), T ), 'c_Lattices_Olower__semilattice__class_Oinf'( W, Z, 'tc_fun'( Y
% 1.23/1.62 , 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), U ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( W, hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.23/1.62 Y, 'tc_bool' ) ) ) ) ), ~( 'c_Finite__Set_Ofinite'( W, Y ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.23/1.62 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.23/1.62 ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.62 ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Osgn__class_Osgn'( Y, X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Osgn__class_Osgn'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.23/1.62 ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~(
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.62 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ),
% 1.23/1.62 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ),
% 1.23/1.62 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 X ), Y ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.62 X ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.62 ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.23/1.62 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.23/1.62 Y, T, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ), =( Z, T ) ],
% 1.23/1.62 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, T ) ), 'c_Pair'(
% 1.23/1.62 U, Y, Z, T ) ), W ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, T )
% 1.23/1.62 ), 'c_Pair'( U, X, Z, T ) ), W ) ) ), ~( 'c_Relation_Osingle__valued'( W
% 1.23/1.62 , Z, T ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, T ), U ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_in'( 'tc_prod'( W, W ) ), 'c_Pair'( Z, U, W, W ) ), V0 ) ) ),
% 1.23/1.62 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( V1, V1 ) ), 'c_Pair'( Y, T, V1,
% 1.23/1.62 V1 ) ), V2 ) ) ), ~( 'c_Equiv__Relations_Ocongruent2'( V2, V0, X, V1, W,
% 1.23/1.62 V3 ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.23/1.62 'c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1'( Z, Y, T, X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( T, X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.23/1.62 'tc_fun'( Y, 'tc_bool' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBB'(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z, X, X, Y ) ), T ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.23/1.62 Y, X ), Z ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Z, X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Z, X ), 'c_COMBB'( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T, X, X, Z ) ), U ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.23/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.23/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP(
% 1.23/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.23/1.62 hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z, 'tc_bool' ), 'tc_bool' ), X
% 1.23/1.62 ), hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z, 'tc_bool' ), 'tc_bool'
% 1.23/1.62 ), Y ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ 'c_lessequals'( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ), 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'(
% 1.23/1.62 X, 'tc_bool' ), 'tc_bool' ), Z ), 'tc_fun'( X, 'tc_bool' ) ), ~(
% 1.23/1.62 'c_lessequals'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.23/1.62 ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), T ), 'c_Relation_OImage'( U
% 1.23/1.62 , 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ), X ), X, Y ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_OImage'( Z,
% 1.23/1.62 'c_Set_Oinsert'( T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U,
% 1.23/1.62 'tc_bool' ) ), U ), U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.23/1.62 U, X ) ), 'c_Pair'( T, Y, U, X ) ), Z ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1'( Y, Z, X ) ), Y
% 1.23/1.62 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Y ) ) ), ~(
% 1.23/1.62 'c_Wellfounded_Owf'( Z, X ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1'( Y, Z, X ) ), Y ) ),
% 1.23/1.62 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Y ) ) ), ~( 'c_Wellfounded_Owf'(
% 1.23/1.62 Z, X ) ) ],
% 1.23/1.62 [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_Wellfounded_Owf'( 'c_Set_Oinsert'(
% 1.23/1.62 'c_Pair'( Z, T, Y, Y ), X, 'tc_prod'( Y, Y ) ), Y ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Relation__XImageE__1__1'( Y, Z, T, X, U ) ), Y ) ),
% 1.23/1.62 ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Relation_OImage'( T, Y, X, U )
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1'( Y, Z, T, X, U ) ), Y )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Relation_OImage'( T, Y, X
% 1.23/1.62 , U ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( 'tc_prod'(
% 1.23/1.62 X, X ), 'tc_bool' ) ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.23/1.62 X, X ) ), Y ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( 'tc_prod'(
% 1.23/1.62 X, X ), 'tc_bool' ) ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.23/1.62 X, X ) ), Y ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), ~( =( hAPP( Y,
% 1.23/1.62 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1'( Z, Y, T, X ) ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ) ) ), =( 'c_Finite__Set_Osetprod'( Y, Z, T,
% 1.23/1.62 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 1.23/1.62 , 'tc_bool' ) ), Z, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( Z, X ) ) ), ~( 'c_lessequals'( T, Z,
% 1.23/1.62 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), Y ), 'c_Transitive__Closure_Otrancl'( T, X )
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.23/1.62 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z
% 1.23/1.62 ) ), X ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ],
% 1.23/1.62 [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.23/1.62 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z
% 1.23/1.62 ) ), X ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, Z, T ) ) ) ),
% 1.23/1.62 ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), 'c_Wellfounded_Oacc'( Z, T ) ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.23/1.62 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, Z ) ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( Z, 't_a' ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, T, Z ) )
% 1.23/1.62 , 'c_Wellfounded_Oacc'( T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y
% 1.23/1.62 ), 'c_Wellfounded_Oacc'( T, Z ) ) ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1'( Y, Z, X ) ),
% 1.23/1.62 'c_Wellfounded_Oacc'( Y, X ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ),
% 1.23/1.62 'c_Wellfounded_Oacc'( Y, X ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, Z, T ) )
% 1.23/1.62 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), 'c_Wellfounded_Oacc'( Z, T
% 1.23/1.62 ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.23/1.62 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, Z ) ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( Z, 't_a' ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1'( Z, Y, X ) ),
% 1.23/1.62 'c_Wellfounded_Oacc'( Z, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, T, Z ) ),
% 1.23/1.62 'c_Wellfounded_Oacc'( T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y )
% 1.23/1.62 , 'c_Wellfounded_Oacc'( T, Z ) ) ) ) ],
% 1.23/1.62 [ 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 1.23/1.62 , X, Y, Y, Y ), 'c_Relation_Orel__comp'( Z, X, Y, Y, Y ), 'tc_fun'(
% 1.23/1.62 'tc_prod'( Y, Y ), 'tc_bool' ) ), Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.23/1.62 'tc_bool' ) ), Y ), ~( 'c_Wellfounded_Owf'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 1.23/1.62 Y, Y ), 'tc_bool' ) ), Y ) ) ],
% 1.23/1.62 [ 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.23/1.62 Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~(
% 1.23/1.62 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 1.23/1.62 , X, Z, Z, Z ), 'c_Relation_Orel__comp'( Y, X, Z, Z, Z ), 'tc_fun'(
% 1.23/1.62 'tc_prod'( Z, Z ), 'tc_bool' ) ), Y, 'tc_fun'( 'tc_prod'( Z, Z ),
% 1.23/1.62 'tc_bool' ) ), Z ) ) ],
% 1.23/1.62 [ =( 'c_Transitive__Closure_Otrancl'( X, Y ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_Orel__comp'(
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( X, Y ), X, Y, Y, Y ), 'tc_fun'(
% 1.23/1.62 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 1.23/1.62 [ =( 'c_Relation_ODomain'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Y,
% 1.23/1.62 Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 1.23/1.62 'tc_prod'( Y, Y ), 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ =( 'c_Transitive__Closure_Ortrancl'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 1.23/1.62 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 1.23/1.62 [ 'c_Relation_Orefl__on'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( Y, X ), X ) ],
% 1.23/1.62 [ =( 'c_Relation_ORange'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y
% 1.23/1.62 ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ 'c_Relation_Oantisym'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Y ),
% 1.23/1.62 ~( 'c_Wellfounded_Oacyclic'( X, Y ) ) ],
% 1.23/1.62 [ 'c_Relation_Osym'( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.23/1.62 'c_Relation_Oconverse'( X, Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool'
% 1.23/1.62 ) ), Y ) ],
% 1.23/1.62 [ =( 'c_Relation_ODomain'( 'c_Relation_OId'( X ), X, X ),
% 1.23/1.62 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ =( 'c_Relation_ORange'( 'c_Relation_OId'( X ), X, X ),
% 1.23/1.62 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.23/1.62 [ 'c_Relation_Orefl__on'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.23/1.62 'tc_bool' ) ), 'c_Relation_OId'( X ), X ) ],
% 1.23/1.62 [ =( 'c_Relation_OImage'( 'c_Relation_OId__on'( X, Y ), Z, Y, Y ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( Y,
% 1.23/1.62 'tc_bool' ) ) ) ],
% 1.23/1.62 [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 1.23/1.62 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ) ],
% 1.23/1.62 [ 'c_Relation_Oantisym'( 'c_Lattices_Oupper__semilattice__class_Osup'( X
% 1.23/1.62 , 'c_Relation_OId'( Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y )
% 1.23/1.62 , ~( 'c_Relation_Oantisym'( X, Y ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.23/1.62 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.23/1.62 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.23/1.62 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X
% 1.23/1.62 ) ), 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1'( T, Z, Y, X ) ), T
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( T,
% 1.23/1.62 Y, X ) ), 'c_Power_Opower__class_Opower'( T, Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), T
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.23/1.62 Z, X ) ), 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.23/1.62 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z )
% 1.23/1.62 , T ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( T,
% 1.23/1.62 Y, X ) ), 'c_Power_Opower__class_Opower'( T, Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), T
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.23/1.62 Z, X ) ), 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, Z, T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.62 Y, 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1'( Z, Y, T, X ) )
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y
% 1.23/1.62 , X ), Z ), T ) ), U ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP(
% 1.23/1.62 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'(
% 1.23/1.62 X, X ), Y ), Y, X, X ), U ) ), T ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.23/1.62 Y, X ), Z ), T ) ), U ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ),
% 1.23/1.62 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Z, X,
% 1.23/1.62 'tc_fun'( X, X ), Y ), Y, X, X ), U ) ), T ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.62 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( Y, Z ),
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, T, U, X ), X ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.62 U ), Z ), T ) ) ), ~( 'c_Finite__Set_Ofinite'( T, U ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBS'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z, X, 'tc_fun'( X, X ), Y ), T, Y, X,
% 1.23/1.62 X ) ), U ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ), hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), T ), U ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBS'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z, X, 'tc_fun'( X, X ), Y ), T, Y, X, X
% 1.23/1.62 ) ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ), hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), T ), U ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_in'( T ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1'( Z, Y, T, X ) ), Z
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), ~( =(
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.62 ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ), =( hAPP( Y,
% 1.23/1.62 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1'( Z, Y, T, X
% 1.23/1.62 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1'( Y, Z, T, X, U ) ), Y
% 1.23/1.62 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, U ) ), T ),
% 1.23/1.62 'c_Product__Type_OSigma'( Y, Z, X, U ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1'( Y, Z, T, X )
% 1.23/1.62 , Z, X, X ) ), T ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.23/1.62 X, X ) ), 'c_Pair'( Y, Z, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T,
% 1.23/1.62 X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1'( Y,
% 1.23/1.62 Z, T, X ), T, X, X ) ), 'c_Transitive__Closure_Ortrancl'( Y, X ) ) ), =(
% 1.23/1.62 Z, T ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, T
% 1.23/1.62 , X, X ) ), 'c_Transitive__Closure_Ortrancl'( Y, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1'( Z,
% 1.23/1.62 Y, T, X ), X, X ) ), Z ) ), =( Y, T ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.62 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 1.23/1.62 X, Z, T, U ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( U, U ) ), 'c_Pair'( Y, Z, U, U ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( T, U ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) )
% 1.23/1.62 , 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 1.23/1.62 X, T, U, Z ), T, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ),
% 1.23/1.62 ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z
% 1.23/1.62 ) ), 'c_Pair'( Y, T, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( U, Z )
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) )
% 1.23/1.62 , 'c_Pair'( T,
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, T,
% 1.23/1.62 U, Z ), Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( X, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ),
% 1.23/1.62 'c_Pair'( T, Y, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ) )
% 1.23/1.62 ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2'( X, Z,
% 1.23/1.62 T, U ) ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.62 'tc_prod'( U, U ) ), 'c_Pair'( Z, Y, U, U ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( T, U ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, Y, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Y, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~(
% 1.23/1.62 'c_Relation_Osingle__valued'( T, X, X ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( X,
% 1.23/1.62 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1'( X, Y, Z ), 't_a',
% 1.23/1.62 't_a' ) ), 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ) ) ), =( Y, X ),
% 1.23/1.62 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( X, Y
% 1.23/1.62 , 't_a', 't_a' ) ), 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ) ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, Z,
% 1.23/1.62 T, U ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.62 'tc_prod'( U, U ) ), 'c_Pair'( Z, Y, U, U ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( T, U ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'(
% 1.23/1.62 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1'( X, Y, Z ), Y, 't_a',
% 1.23/1.62 't_a' ) ), Z ) ), =( Y, X ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.23/1.62 't_a', 't_a' ) ), 'c_Pair'( X, Y, 't_a', 't_a' ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'(
% 1.23/1.62 X, Z, T, U ) ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( U, U ) ), 'c_Pair'( Y, Z, U, U ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( T, U ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1'( Y, Z, T, X )
% 1.23/1.62 , X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), =( Y, Z ), ~(
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) )
% 1.23/1.62 , 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1'( X, U, T ), T
% 1.23/1.62 , T ) ), U ) ) ), ~( 'c_Wellfounded_Owf'( U, T ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1'( X, U, T ), T, T ) ), U
% 1.23/1.62 ) ) ), ~( 'c_Wellfounded_Owf'( U, T ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.23/1.62 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1'( X, U, T ), T, T ) ), U ) )
% 1.23/1.62 ), ~( 'c_Wellfounded_Owf'( U, T ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1'( X, U, T ), T, T ) )
% 1.23/1.62 , U ) ) ), ~( 'c_Wellfounded_Owf'( U, T ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Z, X ), T, 'tc_fun'( Z, X ), 'tc_fun'( 'tc_fun'(
% 1.23/1.62 Z, 'tc_bool' ), X ), Y ), Y, 'tc_fun'( Z, 'tc_bool' ), X ), U ) ), W ),
% 1.23/1.62 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Z, X ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBC'( T, Y, Z, X ), 'tc_fun'( Y, X
% 1.23/1.62 ), 'tc_fun'( 'tc_fun'( Y, 'tc_bool' ), X ), Z ), Z, 'tc_fun'( Y,
% 1.23/1.62 'tc_bool' ), X ), W ) ), U ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X,
% 1.23/1.62 X ) ), Z ) ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1'( Z,
% 1.23/1.62 X ), 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1'(
% 1.23/1.62 Z, X ), X, X ) ), 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1'( Y, Z
% 1.23/1.62 , T, X ), T, X, X ) ), 'c_Transitive__Closure_Otrancl'( Y, X ) ) ), hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, T, X, X ) ), Y ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, T, X, X
% 1.23/1.62 ) ), 'c_Transitive__Closure_Otrancl'( Y, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1'( Z, Y, T, X ),
% 1.23/1.62 X, X ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.23/1.62 'c_Pair'( Y, T, X, X ) ), 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( X,
% 1.23/1.62 'v_sko__Transitive__Closure__Xtrancl__Xcases__1'( X, Y, Z ), 't_a', 't_a'
% 1.23/1.62 ) ), 'c_Transitive__Closure_Otrancl'( Z, 't_a' ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( X, Y, 't_a', 't_a' ) ), Z
% 1.23/1.62 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'(
% 1.23/1.62 X, Y, 't_a', 't_a' ) ), 'c_Transitive__Closure_Otrancl'( Z, 't_a' ) ) ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X,
% 1.23/1.62 X ) ), 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ), ~(
% 1.23/1.62 'c_Wellfounded_Oacyclic'( Z, X ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1'( Y, Z, T, X ),
% 1.23/1.62 Z, X, X ) ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.23/1.62 'c_Pair'( Y, Z, X, X ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.23/1.62 X, X ) ), 'c_Pair'( Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X
% 1.23/1.62 ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1'( Y, Z, T, X ),
% 1.23/1.62 X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ), T ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1'( Y, Z, T, X )
% 1.23/1.62 , T, X, X ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.23/1.62 'c_Pair'( Z, T, X, X ) ), 'c_Transitive__Closure_Otrancl'( Y, X ) ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1'( Z, Y
% 1.23/1.62 , T, X ), X, X ) ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) )
% 1.23/1.62 , 'c_Pair'( Y, T, X, X ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.62 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'(
% 1.23/1.62 'v_sko__Transitive__Closure__Xtrancl__Xcases__1'( X, Y, Z ), Y, 't_a',
% 1.23/1.62 't_a' ) ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) )
% 1.23/1.62 , 'c_Pair'( X, Y, 't_a', 't_a' ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.62 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( X, Y, 't_a', 't_a' ) ),
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( Z, 't_a' ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetprod'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X,
% 1.23/1.62 X ), U, Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, U, Z, X ) ), 'c_Finite__Set_Osetprod'( T, U
% 1.23/1.62 , Z, X ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1'( Z, T, U, W, V0, Y
% 1.23/1.62 , X ), T, X, Y ) ), W ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( V0, Y
% 1.23/1.62 ) ), 'c_Pair'( Z, T, V0, Y ) ), 'c_Relation_Orel__comp'( U, W, V0, X, Y
% 1.23/1.62 ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z,
% 1.23/1.62 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1'( Z, T, U, W, X, V0
% 1.23/1.62 , Y ), X, Y ) ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, V0 )
% 1.23/1.62 ), 'c_Pair'( Z, T, X, V0 ) ), 'c_Relation_Orel__comp'( U, W, X, Y, V0 )
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ =( X, 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__XIdE__1__1'( X, Y ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Relation__XIdE__1__1'( X, Y ), Y, Y ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( 'tc_prod'( Y, Y ) ), X ), 'c_Relation_OId'( Y ) ) ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP(
% 1.23/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( X ), hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBB'(
% 1.23/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z, 'tc_nat', X, Y ) ), T ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ 'c_Wellfounded_Owf'( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1'( X, Y ) ),
% 1.23/1.62 'c_Wellfounded_Oacc'( X, Y ) ) ) ) ],
% 1.23/1.62 [ 'c_Wellfounded_Owf'( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1'( X, Y ) ),
% 1.23/1.62 'c_Wellfounded_Oacc'( X, Y ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~(
% 1.23/1.62 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP(
% 1.23/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( X ), 'c_Finite__Set_Osetprod'( Y, Z
% 1.23/1.62 , T, 'tc_nat' ) ), 'c_Finite__Set_Osetprod'( 'c_COMBB'(
% 1.23/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y, 'tc_nat', X, T ), Z, T, X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.23/1.62 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, Z, X ) ), Y ) ), ~(
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Z ), 'c_Relation_OId__on'(
% 1.23/1.62 Y, X ) ) ) ) ],
% 1.23/1.62 [ =( X, 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, X,
% 1.23/1.62 Z ), 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, X, Z ), Z, Z ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), X ),
% 1.23/1.62 'c_Relation_OId__on'( Y, Z ) ) ) ) ],
% 1.23/1.62 [ =( 'c_Recdef_Ocut'( X, Y, Z, T, U ), 'c_Recdef_Ocut'( W, Y, Z, T, U )
% 1.23/1.62 ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'(
% 1.23/1.62 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X, W, Y, Z, T, U ), Z, T, T ) ),
% 1.23/1.62 Y ) ) ],
% 1.23/1.62 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 1.23/1.62 'tc_prod'( Y, Y ), 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ =( 'c_Transitive__Closure_Otrancl'(
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 1.23/1.62 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 1.23/1.62 [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 1.23/1.62 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 1.23/1.62 [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_OId'( Y ),
% 1.23/1.62 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'( X, Y ), X, Y,
% 1.23/1.62 Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X
% 1.23/1.62 , Y, Y ), X, Y, Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~(
% 1.23/1.62 'c_Relation_Orefl__on'( Z, X, Y ) ) ],
% 1.23/1.62 [ =( 'c_Relation_ORange'( 'v_r', 't_a', 't_b' ), 'c_Relation_ODomain'(
% 1.23/1.62 'c_Relation_Oconverse'( 'v_r', 't_a', 't_b' ), 't_b', 't_a' ) ) ],
% 1.23/1.62 [ 'c_Relation_Oirrefl'( X, Y ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Y
% 1.23/1.62 , Y ) ), 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1'( X
% 1.23/1.62 , Y ), 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1'( X, Y ), Y, Y )
% 1.23/1.62 ), X ) ) ],
% 1.23/1.62 [ 'c_Equiv__Relations_Ocongruent'( X, hAPP( Y, Z ), T, U ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( W ), Z ), V0 ) ) ), ~(
% 1.23/1.62 'c_Equiv__Relations_Ocongruent2'( V1, X, Y, W, T, U ) ), ~(
% 1.23/1.62 'c_Equiv__Relations_Oequiv'( V0, V1, W ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Wellfounded_Omlex__prod'( T, U, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ), U ) ) ), ~(
% 1.23/1.62 'c_lessequals'( hAPP( T, Y ), hAPP( T, Z ), 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_Nitpick_Orefl_H'( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.23/1.62 Y, Y ) ), 'c_Pair'( 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1'( X, Y )
% 1.23/1.62 , 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1'( X, Y ), Y, Y ) ), X ) )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.23/1.62 Z, X ) ), 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.62 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'tc_nat' ), T ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, Z, T, X ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T
% 1.23/1.62 ), 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1'( Z, Y, T, X )
% 1.23/1.62 ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X )
% 1.23/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.23/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 'tc_nat' ) ), Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), ~( =(
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.62 ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ), hBOOL( hAPP( hAPP( 'c_in'( T )
% 1.23/1.62 , 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1'( Z, Y, T,
% 1.23/1.62 X ) ), Z ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1'( Z, T, X ), X, X ) ),
% 1.23/1.62 T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), U ), Z ) ) ), ~(
% 1.23/1.62 'c_Wellfounded_Owf'( T, X ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1'( Z, T, X ), X,
% 1.23/1.62 X ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), U ), Z ) ) ), ~(
% 1.23/1.62 'c_Wellfounded_Owf'( T, X ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Relation__XImageE__1__1'( Z, T, U, X, Y ), T, X, Y )
% 1.23/1.62 ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), T ), 'c_Relation_OImage'( U
% 1.23/1.62 , Z, X, Y ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1'( Z, T, U, X, Y ), T, X
% 1.23/1.62 , Y ) ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), T ),
% 1.23/1.62 'c_Relation_OImage'( U, Z, X, Y ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetprod'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z,
% 1.23/1.62 X, X ), U, Z, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ),
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, U, Z, X ) ), 'c_Finite__Set_Osetprod'( T, U
% 1.23/1.62 , Z, X ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z,
% 1.23/1.62 'c_ATP__Linkup_Osko__Relation__XDomainE__1__1'( Z, T, X, Y ), X, Y ) ), T
% 1.23/1.62 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), 'c_Relation_ODomain'( T, X
% 1.23/1.62 , Y ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z,
% 1.23/1.62 'c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1'( Z, T, X, Y ), X, Y )
% 1.23/1.62 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), 'c_Relation_ODomain'(
% 1.23/1.62 T, X, Y ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1'( Y, Z, X ), Z, X
% 1.23/1.62 , X ) ), Y ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), 'c_Wellfounded_Oacc'(
% 1.23/1.62 Y, X ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, U, T ), T
% 1.23/1.62 , T ) ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ),
% 1.23/1.62 'c_Wellfounded_Oacc'( U, T ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( Z,
% 1.23/1.62 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, T ), 't_a', 't_a' ) ), T ) ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( T,
% 1.23/1.62 't_a' ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.23/1.62 , hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1'( Z, Y, X ), Y, X,
% 1.23/1.62 X ) ), Z ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Z ),
% 1.23/1.62 'c_Wellfounded_Oacc'( T, 't_a' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.62 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( Z,
% 1.23/1.62 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, T ), 't_a', 't_a' ) ), T ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( T,
% 1.23/1.62 't_a' ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( Z,
% 1.23/1.62 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, T ), 't_a', 't_a' ) ), T ) )
% 1.23/1.62 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( T,
% 1.23/1.62 't_a' ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Z ),
% 1.23/1.62 'c_Wellfounded_Oacc'( T, 't_a' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.62 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( Z,
% 1.23/1.62 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, T ), 't_a', 't_a' ) ), T ) ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( T,
% 1.23/1.62 't_a' ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.23/1.62 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, U, T ), T, T )
% 1.23/1.62 ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), 'c_Wellfounded_Oacc'(
% 1.23/1.62 U, T ) ) ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X,
% 1.23/1.62 X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~(
% 1.23/1.62 'c_Wellfounded_Owf'( 'c_Set_Oinsert'( 'c_Pair'( Z, Y, X, X ), T,
% 1.23/1.62 'tc_prod'( X, X ) ), X ) ) ],
% 1.23/1.62 [ 'c_Wellfounded_Owf'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, Z ), T,
% 1.23/1.62 'tc_prod'( Z, Z ) ), Z ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) )
% 1.23/1.62 , 'c_Pair'( Y, X, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( T, Z ) ) )
% 1.23/1.62 , ~( 'c_Wellfounded_Owf'( T, Z ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Relation__XRangeE__1__1'( Z, T, Y, X ), Z, X, Y ) )
% 1.23/1.62 , T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), 'c_Relation_ORange'( T,
% 1.23/1.62 X, Y ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Relation__XRange__iff__1__1'( Z, T, Y, X ), Z, X, Y
% 1.23/1.62 ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), 'c_Relation_ORange'(
% 1.23/1.62 T, X, Y ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1'( Z, Y, T, X )
% 1.23/1.62 , X, X ) ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.23/1.62 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1'( Y, Z, T, X ),
% 1.23/1.62 T, X, X ) ), 'c_Transitive__Closure_Ortrancl'( Y, X ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, T, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( Y, X ) ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y, 'tc_bool' ), Z
% 1.23/1.62 ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X
% 1.23/1.62 , X ) ), Y, X, X ), U ), W, Y, X ), 'c_Power_Opower__class_Opower'( U,
% 1.23/1.62 'c_Finite__Set_Ocard'( W, Y ), X ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z )
% 1.23/1.62 , W ) ), ~( 'c_Finite__Set_Ofinite'( W, Y ) ) ],
% 1.23/1.62 [ =( 'c_Set_Ovimage'( hAPP( 'c_COMBC'( hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y, 'tc_bool'
% 1.23/1.62 ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), Y
% 1.23/1.62 , X, 'tc_fun'( X, X ) ), T ), Y, X, X ), U ), W, Y, X ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), Z ) ), ~(
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_in'( X ), U ), W ) ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.62 X ), T ), W ) ) ],
% 1.23/1.62 [ =( 'c_Set_Ovimage'( hAPP( 'c_COMBC'( hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y, 'tc_bool'
% 1.23/1.62 ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), Y
% 1.23/1.62 , X, 'tc_fun'( X, X ) ), T ), Y, X, X ), U ), W, Y, X ),
% 1.23/1.62 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( X ), U ), W ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X )
% 1.23/1.62 , T ), W ) ) ) ],
% 1.23/1.62 [ =( 'c_Set_Ovimage'( hAPP( 'c_COMBC'( hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y, 'tc_bool'
% 1.23/1.62 ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), Y
% 1.23/1.62 , X, 'tc_fun'( X, X ) ), T ), Y, X, X ), U ), W, Y, X ),
% 1.23/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_in'( X ), U ), W ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), T ), W ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), Z ),
% 1.23/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( T, U, 'tc_fun'( Y,
% 1.23/1.62 'tc_bool' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP(
% 1.23/1.62 'c_COMBC'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'(
% 1.23/1.62 'c_in'( Y ), Y, 'tc_fun'( Y, 'tc_bool' ), 'tc_bool' ), U ), 'tc_bool',
% 1.23/1.62 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), Z, Y, X, 'tc_fun'( X, X ) ), Y, X,
% 1.23/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), T ) ), ~(
% 1.23/1.62 'c_Finite__Set_Ofinite'( T, Y ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.23/1.62 ), 'c_Relation_Oconverse'( U, Y, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.62 'tc_prod'( Y, X ) ), 'c_Pair'( T, Z, Y, X ) ), U ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.23/1.62 ), 'c_Relation_Oconverse'( U, Y, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.62 'tc_prod'( Y, X ) ), 'c_Pair'( T, Z, Y, X ) ), U ) ) ) ],
% 1.23/1.62 [ =( hAPP( 'c_Recdef_Ocut'( X, Y, Z, T, U ), W ), hAPP( X, W ) ), ~(
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( W, Z, T, T ) )
% 1.23/1.62 , Y ) ) ) ],
% 1.23/1.62 [ =( hAPP( 'c_Recdef_Ocut'( X, Y, Z, T, U ), W ), hAPP( X, W ) ), ~(
% 1.23/1.62 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( W, Z, T, T ) )
% 1.23/1.62 , Y ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_OIf'( X ), hAPP( 'c_fequal'( Y ), Z ), 'tc_bool', 'tc_fun'( X,
% 1.23/1.62 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X ) ), Y, X, X ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ) ), U, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.62 ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U ) ), ~(
% 1.23/1.62 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_OIf'( X ), hAPP( 'c_fequal'( Y ), Z ), 'tc_bool', 'tc_fun'( X,
% 1.23/1.62 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X ) ), Y, X, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), U ), hAPP( T, Z ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_in'( Y ), Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_OIf'( X ), hAPP( 'c_fequal'( Y ), Z ), 'tc_bool', 'tc_fun'( X,
% 1.23/1.62 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X ) ), Y, X, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), U ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U ) ), ~(
% 1.23/1.62 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_OIf'( X ), hAPP( 'c_fequal'( Y ), Z ), 'tc_bool', 'tc_fun'( X,
% 1.23/1.62 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X ) ), Y, X, X ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ) ), U, Y, X ), hAPP( T, Z ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( Y ), Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Y )
% 1.23/1.62 ) ],
% 1.23/1.62 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.23/1.62 X, Y, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( T, Z ) ) ) ), hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( Z ), X ), 'c_Relation_ODomain'( T, Z, Z ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ODomain'( Z, X, X ) )
% 1.23/1.62 ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X
% 1.23/1.62 ) ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X
% 1.23/1.62 ) ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_in'( X ), T ), 'c_Wellfounded_Oacc'( Z, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), 'c_Wellfounded_Oacc'( Z, X ) )
% 1.23/1.62 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T,
% 1.23/1.62 X, X ) ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), Y ), Z ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.62 'tc_prod'( X, X ) ), Y ), Z ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ), T ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ), T ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ), =( Y, Z ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), =( Y, Z ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), =( Y, Z ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Transitive__Closure_Ortrancl'( 'c_Relation_Oconverse'( T, X, X ),
% 1.23/1.62 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z,
% 1.23/1.62 Y, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, Y, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( 'c_Relation_Oconverse'( T, X, X ), X )
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Relation_Oconverse'( 'c_Transitive__Closure_Otrancl'( T, X ), X, X
% 1.23/1.62 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z
% 1.23/1.62 , X, X ) ), 'c_Transitive__Closure_Otrancl'( 'c_Relation_Oconverse'( T, X
% 1.23/1.62 , X ), X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Transitive__Closure_Otrancl'( 'c_Relation_Oconverse'( T, X, X ), X
% 1.23/1.62 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z
% 1.23/1.62 , X, X ) ), 'c_Relation_Oconverse'( 'c_Transitive__Closure_Otrancl'( T, X
% 1.23/1.62 ), X, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.23/1.62 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.23/1.62 [ ~( =( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool' ),
% 1.23/1.62 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool'
% 1.23/1.62 ), 'tc_bool' ), Z ) ) ), =( Y, Z ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.23/1.62 , ~( 'c_Wellfounded_Owf'( Z, X ) ) ],
% 1.23/1.62 [ 'c_Relation_Osym'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y ), ~(
% 1.23/1.62 'c_Relation_Osym'( X, Y ) ) ],
% 1.23/1.62 [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ), 'c_Finite__Set_Ofinite'(
% 1.23/1.62 Y, X ) ],
% 1.23/1.62 [ 'c_Relation_Osym'( X, Y ), ~( 'c_Relation_Osym'(
% 1.23/1.62 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 1.23/1.62 [ 'c_Relation_Osym'( 'c_Relation_Oconverse'( X, Y, Y ), Y ), ~(
% 1.23/1.62 'c_Relation_Osym'( X, Y ) ) ],
% 1.23/1.62 [ =( 'c_Relation_ODomain'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y
% 1.23/1.62 ), 'c_Relation_ODomain'( X, Y, Y ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), ~( =( hAPP( Y,
% 1.23/1.62 Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T
% 1.23/1.62 ), Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, U, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), ~( =( hAPP( Y, Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Z
% 1.23/1.62 ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, U, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.23/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ 'c_Relation_Osym'( 'c_Relation_OId'( X ), X ) ],
% 1.23/1.62 [ =( 'c_Relation_Orel__comp'( 'c_Relation_OId'( X ), Y, X, X, Z ), Y ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ =( 'c_Relation_Orel__comp'( X, 'c_Relation_OId'( Y ), Z, Y, Y ), X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ 'c_Relation_Oantisym'( 'c_Relation_OId__on'( X, Y ), Y ) ],
% 1.23/1.62 [ 'c_Wellfounded_Owf'( 'c_Relation_Oconverse'(
% 1.23/1.62 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y ), Y ), ~(
% 1.23/1.62 'c_Wellfounded_Owf'( 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 1.23/1.62 [ 'c_Relation_Orefl__on'( X, Y, Z ), ~( 'c_Relation_Orefl__on'( X,
% 1.23/1.62 'c_Relation_Oconverse'( Y, Z, Z ), Z ) ) ],
% 1.23/1.62 [ 'c_Relation_Orefl__on'( X, 'c_Relation_Oconverse'( Y, Z, Z ), Z ), ~(
% 1.23/1.62 'c_Relation_Orefl__on'( X, Y, Z ) ) ],
% 1.23/1.62 [ 'c_Relation_Osym'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Y ), ~(
% 1.23/1.62 'c_Relation_Osym'( X, Y ) ) ],
% 1.23/1.62 [ 'c_Wellfounded_Owf'( 'c_Relation_Orel__comp'( X, X, Y, Y, Y ), Y ),
% 1.23/1.62 ~( 'c_Wellfounded_Owf'( X, Y ) ) ],
% 1.23/1.62 [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_Wellfounded_Owf'(
% 1.23/1.62 'c_Relation_Orel__comp'( X, X, Y, Y, Y ), Y ) ) ],
% 1.23/1.62 [ =( 'c_Relation_OImage'( 'c_Relation_OId'( X ), Y, X, X ), Y ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.23/1.62 [ =( 'c_Relation_ODomain'( 'c_Relation_OId__on'( X, Y ), Y, Y ), X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ =( 'c_Relation_Oconverse'( X, Y, Y ), X ), ~( 'c_Relation_Osym'( X, Y
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( =( 'c_Relation_Oconverse'( X, Y, Y ), X ) ), 'c_Relation_Osym'( X,
% 1.23/1.62 Y ) ],
% 1.23/1.62 [ =( 'c_Relation_ORange'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y
% 1.23/1.62 ), 'c_Relation_ORange'( X, Y, Y ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.62 'c_Finite__Set_Ofinite'( Z, T ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.62 'c_Finite__Set_Ofinite'( Z, T ) ],
% 1.23/1.62 [ =( 'c_Relation_Oconverse'( 'c_Relation_Orel__comp'( X, Y, Z, T, U ), Z
% 1.23/1.62 , U ), 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( Y, T, U ),
% 1.23/1.62 'c_Relation_Oconverse'( X, Z, T ), U, T, Z ) ) ],
% 1.23/1.62 [ 'c_Relation_Osym'( 'c_Relation_OId__on'( X, Y ), Y ) ],
% 1.23/1.62 [ 'c_Relation_Orefl__on'( X, 'c_Relation_OId__on'( X, Y ), Y ) ],
% 1.23/1.62 [ 'c_Wellfounded_Owf'( 'c_Relation_Oinv__image'( X, Y, Z, T ), T ), ~(
% 1.23/1.62 'c_Wellfounded_Owf'( X, Z ) ) ],
% 1.23/1.62 [ =( 'c_Relation_Orel__comp'( X, 'c_Transitive__Closure_Ortrancl'( X, Y
% 1.23/1.62 ), Y, Y, Y ), 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'(
% 1.23/1.62 X, Y ), X, Y, Y, Y ) ) ],
% 1.23/1.62 [ 'c_Relation_Osym'( 'c_Relation_Oinv__image'( X, Y, Z, T ), T ), ~(
% 1.23/1.62 'c_Relation_Osym'( X, Z ) ) ],
% 1.23/1.62 [ =( 'c_Transitive__Closure_Otrancl'( 'c_Transitive__Closure_Ortrancl'(
% 1.23/1.62 X, Y ), Y ), 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 1.23/1.62 [ =( 'c_Relation_Oconverse'( 'c_Relation_OId'( X ), X, X ),
% 1.23/1.62 'c_Relation_OId'( X ) ) ],
% 1.23/1.62 [ 'c_Wellfounded_Owf'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y ), ~(
% 1.23/1.62 'c_Wellfounded_Owf'( X, Y ) ) ],
% 1.23/1.62 [ =( 'c_Relation_Orel__comp'( 'c_Relation_Orel__comp'( X, Y, Z, T, U ),
% 1.23/1.62 W, Z, U, V0 ), 'c_Relation_Orel__comp'( X, 'c_Relation_Orel__comp'( Y, W
% 1.23/1.62 , T, U, V0 ), Z, T, V0 ) ) ],
% 1.23/1.62 [ =( 'c_Relation_Oconverse'( 'c_Relation_Oinv__image'( X, Y, Z, T ), T,
% 1.23/1.62 T ), 'c_Relation_Oinv__image'( 'c_Relation_Oconverse'( X, Z, Z ), Y, Z, T
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ =( 'c_Transitive__Closure_Otrancl'( 'c_Relation_Oconverse'( X, Y, Y )
% 1.23/1.62 , Y ), 'c_Relation_Oconverse'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y
% 1.23/1.62 , Y ) ) ],
% 1.23/1.62 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =( hAPP(
% 1.23/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), hAPP(
% 1.23/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ) ), =( Y, Z ) ],
% 1.23/1.62 [ =( 'c_Relation_Oconverse'( 'c_Relation_OId__on'( X, Y ), Y, Y ),
% 1.23/1.62 'c_Relation_OId__on'( X, Y ) ) ],
% 1.23/1.62 [ ~( =( 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X, Y, Y ), X, Y
% 1.23/1.62 , Y, Y ), X ) ), 'c_Equiv__Relations_Oequiv'( 'c_Relation_ODomain'( X, Y
% 1.23/1.62 , Y ), X, Y ) ],
% 1.23/1.62 [ 'c_Relation_Oantisym'( 'c_Relation_OId'( X ), X ) ],
% 1.23/1.62 [ 'c_Wellfounded_Owf'( 'c_Wellfounded_Omlex__prod'( X, Y, Z ), Z ), ~(
% 1.23/1.62 'c_Wellfounded_Owf'( Y, Z ) ) ],
% 1.23/1.62 [ =( 'c_Relation_ORange'( 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ),
% 1.23/1.62 'c_Relation_ODomain'( X, Y, Z ) ) ],
% 1.23/1.62 [ =( 'c_Relation_ORange'( 'c_Relation_OId__on'( X, Y ), Y, Y ), X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.23/1.62 [ =( 'c_Relation_Oconverse'( 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ),
% 1.23/1.62 X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ), 'c_Finite__Set_Ofinite'( T, Y ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ), 'c_Finite__Set_Ofinite'( T, Y ) ],
% 1.23/1.62 [ =( 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X, Y, Y ), X, Y, Y
% 1.23/1.62 , Y ), X ), ~( 'c_Equiv__Relations_Oequiv'( Z, X, Y ) ) ],
% 1.23/1.62 [ =( 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y, Y ),
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 1.23/1.62 [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'(
% 1.23/1.62 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 1.23/1.62 [ 'c_Relation_Oantisym'( 'c_Relation_Oconverse'( X, Y, Y ), Y ), ~(
% 1.23/1.62 'c_Relation_Oantisym'( X, Y ) ) ],
% 1.23/1.62 [ 'c_Relation_Orefl__on'( X, Y, Z ), ~( 'c_Equiv__Relations_Oequiv'( X,
% 1.23/1.62 Y, Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.23/1.62 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_Relation_Oconverse'( X, Y, Y )
% 1.23/1.62 , Y ), 'c_Relation_Oconverse'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.23/1.62 Y, Y ) ) ],
% 1.23/1.62 [ 'c_Relation_Osym'( X, Y ), ~( 'c_Equiv__Relations_Oequiv'( Z, X, Y ) )
% 1.23/1.62 ],
% 1.23/1.62 [ =( 'c_Relation_ODomain'( 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ),
% 1.23/1.62 'c_Relation_ORange'( X, Y, Z ) ) ],
% 1.23/1.62 [ =( 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_Orel__comp'(
% 1.23/1.62 'c_Transitive__Closure_Ortrancl'( X, Y ), X, Y, Y, Y ) ) ],
% 1.23/1.62 [ =( 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_Orel__comp'( X
% 1.23/1.62 , 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y, Y ) ) ],
% 1.23/1.62 [ =( 'c_Relation_ORange'( X, Y, Z ), 'c_Relation_ODomain'(
% 1.23/1.62 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ) ) ],
% 1.23/1.62 [ 'c_Relation_Ototal__on'( X, Y, Z ), ~( 'c_Relation_Ototal__on'( X,
% 1.23/1.62 'c_Relation_Oconverse'( Y, Z, Z ), Z ) ) ],
% 1.23/1.62 [ 'c_Relation_Ototal__on'( X, 'c_Relation_Oconverse'( Y, Z, Z ), Z ),
% 1.23/1.62 ~( 'c_Relation_Ototal__on'( X, Y, Z ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( X, hAPP( Y, Z ) ) ), ~( hBOOL( hAPP( 'c_Set_Ovimage'( Y,
% 1.23/1.62 X, T, U ), Z ) ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( 'c_Set_Ovimage'( X, Y, Z, T ), U ) ), ~( hBOOL( hAPP( Y,
% 1.23/1.62 hAPP( X, U ) ) ) ) ],
% 1.23/1.62 [ 'c_Wellfounded_Owf'( 'c_Wellfounded_Omeasure'( X, Y ), Y ) ],
% 1.23/1.62 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_Transitive__Closure_Otrancl'(
% 1.23/1.62 X, Y ), Y ), 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 1.23/1.62 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_Transitive__Closure_Ortrancl'(
% 1.23/1.62 X, Y ), Y ), 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.23/1.62 ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Y, X ) ), 'c_Pair'( T
% 1.23/1.62 , Z, Y, X ) ), 'c_Relation_Oconverse'( U, X, Y ) ) ) ) ],
% 1.23/1.62 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X,
% 1.23/1.62 X ) ), Z ) ) ), ~( 'c_Relation_Oirrefl'( Z, X ) ) ],
% 1.23/1.62 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.62 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.62 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ), T ) ) ), ~( hBOOL(
% 1.23/1.62 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.23/1.63 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.63 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.23/1.63 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ), T ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.63 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ), T ) ) ), ~( hBOOL(
% 1.23/1.63 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.23/1.63 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.63 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.23/1.63 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ), T ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.63 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ), T ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.63 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.23/1.63 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.23/1.63 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.23/1.63 ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.23/1.63 ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ],
% 1.23/1.63 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X,
% 1.23/1.63 X ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.23/1.63 'c_Pair'( Z, Y, X, X ) ), T ) ) ), ~( 'c_Wellfounded_Owf'( T, X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.23/1.63 Y, X, Z, Z ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z )
% 1.23/1.63 ), 'c_Pair'( X, Y, Z, Z ) ), T ) ) ), ~( 'c_Relation_Oantisym'( T, Z ) )
% 1.23/1.63 ],
% 1.23/1.63 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.23/1.63 Y, X, Z, Z ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z )
% 1.23/1.63 ), 'c_Pair'( X, Y, Z, Z ) ), T ) ) ), ~( 'c_Relation_Oantisym'( T, Z ) )
% 1.23/1.63 ],
% 1.23/1.63 [ =( hAPP( X, Y ), hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.63 'tc_prod'( T, T ) ), 'c_Pair'( Y, Z, T, T ) ), U ) ) ), ~(
% 1.23/1.63 'c_Equiv__Relations_Ocongruent'( U, X, T, W ) ) ],
% 1.23/1.63 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.23/1.63 X, Y, Z, Z ) ), 'c_Relation_OId__on'( T, Z ) ) ) ) ],
% 1.23/1.63 [ ~( =( 'c_Recdef_Ocut'( X, Y, Z, T, U ), 'c_Recdef_Ocut'( W, Y, Z, T, U
% 1.23/1.63 ) ) ), =( hAPP( X, V0 ), hAPP( W, V0 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.23/1.63 'tc_prod'( T, T ) ), 'c_Pair'( V0, Z, T, T ) ), Y ) ) ) ],
% 1.23/1.63 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.23/1.63 X, Y, Z, Z ) ), 'c_Relation_OId'( Z ) ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.23/1.63 ), Z ) ), ~( 'c_Nitpick_Orefl_H'( Z, X ) ) ],
% 1.23/1.63 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X,
% 1.23/1.63 X ) ), Z ) ) ), ~( 'c_Wellfounded_Owf'( Z, X ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.63 ), 'c_Relation_Oinv__image'( T, U, W, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( W, W ) ), 'c_Pair'( hAPP( U, Y ), hAPP( U, Z ), W, W )
% 1.23/1.63 ), T ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( hAPP( Y, Z )
% 1.23/1.63 , hAPP( Y, T ), X, X ) ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.23/1.63 W, W ) ), 'c_Pair'( Z, T, W, W ) ), 'c_Relation_Oinv__image'( U, Y, X, W
% 1.23/1.63 ) ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.63 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z
% 1.23/1.63 , Y, X, X ) ), T ) ) ), ~( 'c_Relation_Osym'( T, X ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.63 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z
% 1.23/1.63 , Y, X, X ) ), T ) ) ), ~( 'c_Relation_Osym'( T, X ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.23/1.63 ), 'c_Relation_Orel__comp'( U, W, X, V0, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( V0, Y ) ), 'c_Pair'( V1, T, V0, Y ) ), W ) ) ), ~(
% 1.23/1.63 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, V0 ) ), 'c_Pair'( Z, V1, X, V0 )
% 1.23/1.63 ), U ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.63 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ), T ) ) ), ~( hBOOL(
% 1.23/1.63 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ), T ) )
% 1.23/1.63 ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.63 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.23/1.63 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.23/1.63 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.23/1.63 ), 'c_Relation_OId'( X ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.23/1.63 ), 'c_Relation_OId'( X ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.23/1.63 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ), hAPP(
% 1.23/1.63 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.23/1.63 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ), hAPP(
% 1.23/1.63 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.23/1.63 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt' ) ),
% 1.23/1.63 'v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1'( X, Y ) ) ), =( X, Y
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y, 'tc_bool' ), Z
% 1.23/1.63 ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X
% 1.23/1.63 , X ) ), Y, X, X ), 'c_HOL_Oone__class_Oone'( X ) ), U, Y, X ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( X ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U )
% 1.23/1.63 ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y, 'tc_bool' ), Z
% 1.23/1.63 ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X
% 1.23/1.63 , X ) ), Y, X, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), U ), hAPP( T, Z
% 1.23/1.63 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y, 'tc_bool' ), Z
% 1.23/1.63 ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X
% 1.23/1.63 , X ) ), Y, X, X ), 'c_HOL_Oone__class_Oone'( X ) ), U, Y, X ), hAPP( T,
% 1.23/1.63 Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U ) ) ), ~(
% 1.23/1.63 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y, 'tc_bool' ), Z
% 1.23/1.63 ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X
% 1.23/1.63 , X ) ), Y, X, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), U ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U
% 1.23/1.63 ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.23/1.63 [ =( 'c_Set_Ovimage'( hAPP( 'c_COMBC'( hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y, 'tc_bool'
% 1.23/1.63 ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), Y
% 1.23/1.63 , X, 'tc_fun'( X, X ) ), T ), Y, X, X ), U ), W, Y, X ), Z ), hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_in'( X ), U ), W ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), W
% 1.23/1.63 ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.23/1.63 ), 'c_Product__Type_OSigma'( U, W, X, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( Y ), T ), hAPP( W, Z ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.23/1.63 Z ), U ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.23/1.63 ), 'c_Product__Type_OSigma'( U, W, X, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( Y ), T ), hAPP( W, Z ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.23/1.63 Z ), U ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.23/1.63 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X
% 1.23/1.63 ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ),
% 1.23/1.63 'c_Wellfounded_Oacc'( Z, X ) ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.23/1.63 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X
% 1.23/1.63 ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ),
% 1.23/1.63 'c_Wellfounded_Oacc'( Z, X ) ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_OImage'( Z, T, U, X )
% 1.23/1.63 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( U, X ) ), 'c_Pair'( W, Y,
% 1.23/1.63 U, X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), T ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_OImage'( Z, T, U, X )
% 1.23/1.63 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( U, X ) ), 'c_Pair'( W, Y,
% 1.23/1.63 U, X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), T ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ),
% 1.23/1.63 'c_Relation_OId__on'( Z, X ) ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.23/1.63 ), 'c_Relation_OId__on'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.23/1.63 Y ), Z ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( T, Y, X, X ) ), U ) ) ), ~(
% 1.23/1.63 'c_Equiv__Relations_Oequiv'( Z, U, X ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ), U ) ) ), ~(
% 1.23/1.63 'c_Equiv__Relations_Oequiv'( Z, U, X ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ORange'( Z, T, X ) )
% 1.23/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, X ) ), 'c_Pair'( U, Y, T
% 1.23/1.63 , X ) ), Z ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ORange'( Z, T, X ) )
% 1.23/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, X ) ), 'c_Pair'( U, Y, T
% 1.23/1.63 , X ) ), Z ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ODomain'( Z, X, T ) )
% 1.23/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, T ) ), 'c_Pair'( Y, U, X
% 1.23/1.63 , T ) ), Z ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ODomain'( Z, X, T ) )
% 1.23/1.63 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, T ) ), 'c_Pair'( Y, U, X
% 1.23/1.63 , T ) ), Z ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP(
% 1.23/1.63 hAPP( 'c_in'( 'tc_prod'( U, X ) ), 'c_Pair'( T, Y, U, X ) ),
% 1.23/1.63 'c_Product__Type_OSigma'( W, Z, U, X ) ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, T ) ), 'c_Pair'( Y, U, X, T ) ),
% 1.23/1.63 'c_Product__Type_OSigma'( Z, W, X, T ) ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.63 ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, Y
% 1.23/1.63 , X, X ) ), T ) ), =( Z, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), U )
% 1.23/1.63 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), U ) ) ), ~(
% 1.23/1.63 'c_Relation_Ototal__on'( U, T, X ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.23/1.63 ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.23/1.63 'c_Relation_Orefl__on'( T, Z, X ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( T, Y, X, X ) ), U ) ) ), ~(
% 1.23/1.63 'c_Relation_Orefl__on'( Z, U, X ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ), U ) ) ), ~(
% 1.23/1.63 'c_Relation_Orefl__on'( Z, U, X ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.23/1.63 ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.23/1.63 'c_Relation_Orefl__on'( T, Z, X ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.63 ), 'c_Wellfounded_Omlex__prod'( T, U, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( T, Y ) ), hAPP( T, Z ) ) ) )
% 1.23/1.63 ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.23/1.63 ), 'c_Wellfounded_Omeasure'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( T, Y ) ), hAPP( T, Z ) ) ) )
% 1.23/1.63 ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( X, Y )
% 1.23/1.63 ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ),
% 1.23/1.63 'c_Pair'( Y, Z, T, T ) ), 'c_Wellfounded_Omeasure'( X, T ) ) ) ) ],
% 1.23/1.63 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.23/1.63 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.23/1.63 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.23/1.63 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.23/1.63 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( hAPP(
% 1.23/1.63 'c_Arrow__Order__Mirabelle_Omktop', Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.23/1.63 , Z ) ) ), =( X, Y ), =( X, T ) ],
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.23/1.63 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( hAPP(
% 1.23/1.63 'c_Arrow__Order__Mirabelle_Omktop', Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.23/1.63 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.23/1.63 , Z ) ) ), =( Y, T ), =( X, T ) ],
% 1.23/1.63 [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) ), =( Y, W ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) ), =( X, U ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.23/1.63 , 'c_Pair'( 'v_c____', 'v_d____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( 'v_P____' ) ) ), ~( hBOOL(
% 1.23/1.63 hAPP( hAPP( 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
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% 1.23/1.63 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
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% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
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% 1.23/1.63 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
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% 1.23/1.63 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
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% 1.23/1.63 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ) ) ],
% 1.23/1.63 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.23/1.63 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.23/1.63 , 'c_Pair'( 'v_e____', 'v_d____', 'tc_Arrow__Order__Mirabelle_Oalt',
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% 1.23/1.63 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
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% 1.23/1.63 [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_HOL_Oord'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Lattices_Oboolean__algebra'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Orderings_Otop'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_HOL_Oord'( 'tc_bool' ) ],
% 1.23/1.63 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.23/1.63 , W ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP( hAPP( X, W ),
% 1.23/1.63 U ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 1.23/1.63 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 1.23/1.63 ] .
% 1.23/1.63
% 1.23/1.63
% 1.23/1.63 percentage equality = 0.185230, percentage horn = 0.851151
% 1.23/1.63 This is a problem with some equality
% 1.23/1.63
% 1.23/1.63
% 1.23/1.63
% 1.23/1.63 Options Used:
% 1.23/1.63
% 1.23/1.63 useres = 1
% 1.23/1.63 useparamod = 1
% 1.23/1.63 useeqrefl = 1
% 1.23/1.63 useeqfact = 1
% 1.23/1.63 usefactor = 1
% 1.23/1.63 usesimpsplitting = 0
% 1.23/1.63 usesimpdemod = 5
% 1.23/1.63 usesimpres = 3
% 1.23/1.63
% 1.23/1.63 resimpinuse = 1000
% 1.23/1.63 resimpclauses = 20000
% 1.23/1.63 substype = eqrewr
% 1.23/1.63 backwardsubs = 1
% 1.23/1.63 selectoldest = 5
% 1.23/1.63
% 1.23/1.63 litorderings [0] = split
% 1.23/1.63 litorderings [1] = extend the termordering, first sorting on arguments
% 1.23/1.63
% 1.23/1.63 termordering = kbo
% 1.23/1.63
% 1.23/1.63 litapriori = 0
% 1.23/1.63 termapriori = 1
% 1.23/1.63 litaposteriori = 0
% 1.23/1.63 termaposteriori = 0
% 1.23/1.63 demodaposteriori = 0
% 1.23/1.63 ordereqreflfact = 0
% 1.23/1.63
% 1.23/1.63 litselect = negord
% 1.23/1.63
% 1.23/1.63 maxweight = 15
% 1.23/1.63 maxdepth = 30000
% 1.23/1.63 maxlength = 115
% 1.23/1.63 maxnrvars = 195
% 1.23/1.63 excuselevel = 1
% 1.23/1.63 increasemaxweight = 1
% 1.23/1.63
% 1.23/1.63 maxselected = 10000000
% 1.23/1.63 maxnrclauses = 10000000
% 1.23/1.63
% 1.23/1.63 showgenerated = 0
% 1.23/1.63 showkept = 0
% 1.23/1.63 showselected = 0
% 1.23/1.63 showdeleted = 0
% 1.23/1.63 showresimp = 1
% 1.23/1.63 showstatus = 2000
% 1.23/1.63
% 1.23/1.63 prologoutput = 1
% 1.23/1.63 nrgoals = 5000000
% 1.23/1.63 totalproof = 1
% 1.23/1.63
% 1.23/1.63 Symbols occurring in the translation:
% 1.23/1.63
% 1.23/1.63 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.23/1.63 . [1, 2] (w:1, o:190, a:1, s:1, b:0),
% 1.23/1.63 ! [4, 1] (w:0, o:101, a:1, s:1, b:0),
% 1.23/1.63 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.23/1.63 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.23/1.63 'class_Ring__and__Field_Oordered__field' [40, 1] (w:1, o:110, a:1, s:
% 1.23/1.63 1, b:0),
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero' [41, 1] (w:1, o:115, a:1
% 1.23/1.63 , s:1, b:0),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero' [42, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.23/1.63 'c_lessequals' [44, 3] (w:1, o:242, a:1, s:1, b:0),
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide' [45, 1] (w:1, o:117, a:1, s:1, b:0),
% 1.23/1.63
% 1.23/1.63 hAPP [47, 2] (w:1, o:215, a:1, s:1, b:0),
% 1.23/1.63 'class_Ring__and__Field_Ocomm__semiring__1' [48, 1] (w:1, o:113, a:1
% 1.23/1.63 , s:1, b:0),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus' [49, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.23/1.63 'class_OrderedGroup_Ocomm__monoid__add' [52, 1] (w:1, o:122, a:1, s:1
% 1.23/1.63 , b:0),
% 1.23/1.63 'tc_bool' [55, 0] (w:1, o:24, a:1, s:1, b:0),
% 1.23/1.63 'tc_fun' [56, 2] (w:1, o:216, a:1, s:1, b:0),
% 1.23/1.63 'c_Orderings_Obot__class_Obot' [57, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.23/1.63 'c_Lattices_Olower__semilattice__class_Oinf' [58, 3] (w:1, o:243, a:1
% 1.23/1.63 , s:1, b:0),
% 1.23/1.63 'class_Lattices_Obounded__lattice' [60, 1] (w:1, o:125, a:1, s:1, b:0
% 1.23/1.63 ),
% 1.23/1.63 'class_Ring__and__Field_Oordered__ring__strict' [61, 1] (w:1, o:126
% 1.23/1.63 , a:1, s:1, b:0),
% 1.23/1.63 'c_HOL_Otimes__class_Otimes' [62, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.23/1.63 'c_Transitive__Closure_Ortrancl' [64, 2] (w:1, o:217, a:1, s:1, b:0)
% 1.23/1.63 ,
% 1.23/1.63 'tc_prod' [66, 2] (w:1, o:218, a:1, s:1, b:0),
% 1.23/1.63 'c_HOL_Oone__class_Oone' [67, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup' [68, 3] (w:1, o:244, a:1
% 1.23/1.63 , s:1, b:0),
% 1.23/1.63 'c_Relation_Osym' [69, 2] (w:1, o:219, a:1, s:1, b:0),
% 1.23/1.63 'c_Pair' [71, 4] (w:1, o:269, a:1, s:1, b:0),
% 1.23/1.63 'c_Set_Oinsert' [72, 3] (w:1, o:252, a:1, s:1, b:0),
% 1.23/1.63 'c_Relation_ODomain' [73, 3] (w:1, o:245, a:1, s:1, b:0),
% 1.23/1.63 'c_HOL_Ouminus__class_Ouminus' [74, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.23/1.63 hBOOL [75, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.23/1.63 'class_Ring__and__Field_Opordered__ring' [76, 1] (w:1, o:135, a:1, s:
% 1.23/1.63 1, b:0),
% 1.23/1.63 'c_HOL_Ominus__class_Ominus' [77, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.23/1.63 'class_Ring__and__Field_Oordered__semidom' [80, 1] (w:1, o:130, a:1
% 1.23/1.63 , s:1, b:0),
% 1.23/1.63 'c_Power_Opower__class_Opower' [82, 3] (w:1, o:253, a:1, s:1, b:0),
% 1.23/1.63 'tc_nat' [84, 0] (w:1, o:46, a:1, s:1, b:0),
% 1.23/1.63 'class_OrderedGroup_Olordered__ab__group__add' [85, 1] (w:1, o:137
% 1.23/1.63 , a:1, s:1, b:0),
% 1.23/1.63 'c_Relation_OImage' [87, 4] (w:1, o:270, a:1, s:1, b:0),
% 1.23/1.63 'c_Ring__and__Field_Odvd__class_Odvd' [89, 3] (w:1, o:246, a:1, s:1
% 1.23/1.63 , b:0),
% 1.23/1.63 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [90, 1]
% 1.23/1.63 (w:1, o:139, a:1, s:1, b:0),
% 1.23/1.63 'c_in' [92, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.23/1.63 'c_Set_Ovimage' [94, 4] (w:1, o:272, a:1, s:1, b:0),
% 1.23/1.63 'c_Orderings_Otop__class_Otop' [95, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.23/1.63 'class_Orderings_Obot' [96, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.23/1.63 'c_Finite__Set_Osetsum' [97, 2] (w:1, o:220, a:1, s:1, b:0),
% 1.23/1.63 'c_Finite__Set_Ofinite' [99, 2] (w:1, o:221, a:1, s:1, b:0),
% 1.23/1.63 'class_Ring__and__Field_Oring' [100, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.23/1.63
% 1.23/1.63 'class_OrderedGroup_Opordered__ab__group__add' [101, 1] (w:1, o:144
% 1.23/1.63 , a:1, s:1, b:0),
% 1.23/1.63 'class_Ring__and__Field_Oordered__semiring__strict' [103, 1] (w:1, o:
% 1.23/1.63 131, a:1, s:1, b:0),
% 1.23/1.63 'c_HOL_Oord__class_Oless' [104, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.23/1.63 'class_Ring__and__Field_Oidom' [106, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.23/1.63
% 1.23/1.63 'class_OrderedGroup_Oordered__ab__group__add' [108, 1] (w:1, o:138
% 1.23/1.63 , a:1, s:1, b:0),
% 1.23/1.63 'class_Ring__and__Field_Oring__1' [109, 1] (w:1, o:146, a:1, s:1, b:0
% 1.23/1.63 ),
% 1.23/1.63 'class_Int_Onumber__ring' [110, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.23/1.63 'class_Ring__and__Field_Oordered__semiring' [112, 1] (w:1, o:132, a:1
% 1.23/1.63 , s:1, b:0),
% 1.23/1.63 'class_OrderedGroup_Oab__group__add' [113, 1] (w:1, o:149, a:1, s:1
% 1.23/1.63 , b:0),
% 1.23/1.63 'class_OrderedGroup_Ogroup__add' [114, 1] (w:1, o:150, a:1, s:1, b:0)
% 1.23/1.63 ,
% 1.23/1.63 'class_Ring__and__Field_Ocomm__ring__1' [115, 1] (w:1, o:111, a:1, s:
% 1.23/1.63 1, b:0),
% 1.23/1.63 'class_OrderedGroup_Omonoid__mult' [117, 1] (w:1, o:153, a:1, s:1, b:
% 1.23/1.63 0),
% 1.23/1.63 'class_Ring__and__Field_Odvd' [118, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.23/1.63 'class_OrderedGroup_Ocomm__monoid__mult' [119, 1] (w:1, o:155, a:1
% 1.23/1.63 , s:1, b:0),
% 1.23/1.63 'c_Finite__Set_Osetprod' [120, 4] (w:1, o:274, a:1, s:1, b:0),
% 1.23/1.63 'class_OrderedGroup_Opordered__comm__monoid__add' [121, 1] (w:1, o:
% 1.23/1.63 156, a:1, s:1, b:0),
% 1.23/1.63 'c_Finite__Set_Ocard' [122, 2] (w:1, o:222, a:1, s:1, b:0),
% 1.23/1.63 'class_Ring__and__Field_Ofield' [123, 1] (w:1, o:157, a:1, s:1, b:0)
% 1.23/1.63 ,
% 1.23/1.63 'class_Ring__and__Field_Oring__no__zero__divisors' [124, 1] (w:1, o:
% 1.23/1.63 158, a:1, s:1, b:0),
% 1.23/1.63 'class_Ring__and__Field_Ono__zero__divisors' [125, 1] (w:1, o:109, a:
% 1.23/1.63 1, s:1, b:0),
% 1.23/1.63 'c_Wellfounded_Owf' [126, 2] (w:1, o:223, a:1, s:1, b:0),
% 1.23/1.63 'c_Relation_Orel__comp' [127, 5] (w:1, o:295, a:1, s:1, b:0),
% 1.23/1.63 'c_Relation_ORange' [128, 3] (w:1, o:247, a:1, s:1, b:0),
% 1.23/1.63 'c_Relation_Osingle__valued' [130, 3] (w:1, o:249, a:1, s:1, b:0),
% 1.23/1.63 'c_Relation_Orefl__on' [131, 3] (w:1, o:248, a:1, s:1, b:0),
% 1.23/1.63 'class_Lattices_Olattice' [132, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.23/1.63 'class_Lattices_Olower__semilattice' [133, 1] (w:1, o:160, a:1, s:1
% 1.23/1.63 , b:0),
% 1.23/1.63 'c_Relation_OId' [135, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.23/1.63 'class_Lattices_Oboolean__algebra' [140, 1] (w:1, o:162, a:1, s:1, b:
% 1.23/1.63 0),
% 1.23/1.63 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1' [143, 3] (w:1
% 1.23/1.63 , o:254, a:1, s:1, b:0),
% 1.23/1.63 'c_Nat_Osemiring__1__class_Oof__nat' [144, 1] (w:1, o:123, a:1, s:1
% 1.23/1.63 , b:0),
% 1.23/1.63 'class_Ring__and__Field_Osemiring__0' [145, 1] (w:1, o:164, a:1, s:1
% 1.23/1.63 , b:0),
% 1.23/1.63 'class_Power_Opower' [146, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.23/1.63 'class_Orderings_Olinorder' [147, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.23/1.63 'class_OrderedGroup_Opordered__ab__semigroup__add' [148, 1] (w:1, o:
% 1.23/1.63 166, a:1, s:1, b:0),
% 1.23/1.63 'class_Lattices_Odistrib__lattice' [149, 1] (w:1, o:178, a:1, s:1, b:
% 1.23/1.63 0),
% 1.23/1.63 'class_OrderedGroup_Olordered__ab__group__add__join' [150, 1] (w:1
% 1.23/1.63 , o:151, a:1, s:1, b:0),
% 1.23/1.63 'class_Lattices_Oupper__semilattice' [151, 1] (w:1, o:179, a:1, s:1
% 1.23/1.63 , b:0),
% 1.23/1.63 'class_Ring__and__Field_Osgn__if' [154, 1] (w:1, o:180, a:1, s:1, b:0
% 1.23/1.63 ),
% 1.23/1.63 'c_HOL_Osgn__class_Osgn' [155, 2] (w:1, o:224, a:1, s:1, b:0),
% 1.23/1.63 'class_OrderedGroup_Oab__semigroup__add' [156, 1] (w:1, o:167, a:1
% 1.23/1.63 , s:1, b:0),
% 1.23/1.63 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1' [158, 3] (w:1, o:255
% 1.23/1.63 , a:1, s:1, b:0),
% 1.23/1.63 'class_Ring__and__Field_Ozero__neq__one' [159, 1] (w:1, o:181, a:1
% 1.23/1.63 , s:1, b:0),
% 1.23/1.63 'class_Ring__and__Field_Omult__zero' [160, 1] (w:1, o:106, a:1, s:1
% 1.23/1.63 , b:0),
% 1.23/1.63 'c_Relation_Oconverse' [162, 3] (w:1, o:250, a:1, s:1, b:0),
% 1.23/1.64 'class_OrderedGroup_Olordered__ab__group__add__meet' [163, 1] (w:1
% 1.23/1.64 , o:152, a:1, s:1, b:0),
% 1.23/1.64 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1' [168, 3] (w:1, o:
% 1.23/1.64 256, a:1, s:1, b:0),
% 1.23/1.64 'c_Wellfounded_Oacyclic' [169, 2] (w:1, o:225, a:1, s:1, b:0),
% 1.23/1.64 'class_Orderings_Oorder' [170, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Oordered__idom' [171, 1] (w:1, o:133, a:1, s:
% 1.23/1.64 1, b:0),
% 1.23/1.64 'class_OrderedGroup_Oab__semigroup__idem__mult' [172, 1] (w:1, o:169
% 1.23/1.64 , a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Oring__1__no__zero__divisors' [173, 1] (w:1
% 1.23/1.64 , o:163, a:1, s:1, b:0),
% 1.23/1.64 'c_Equiv__Relations_Oequiv' [174, 3] (w:1, o:257, a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Osemiring' [175, 1] (w:1, o:182, a:1, s:1, b:
% 1.23/1.64 0),
% 1.23/1.64 'class_Ring__and__Field_Opordered__cancel__semiring' [176, 1] (w:1
% 1.23/1.64 , o:183, a:1, s:1, b:0),
% 1.23/1.64 'c_Product__Type_OSigma' [179, 4] (w:1, o:275, a:1, s:1, b:0),
% 1.23/1.64 'class_OrderedGroup_Ocancel__ab__semigroup__add' [180, 1] (w:1, o:170
% 1.23/1.64 , a:1, s:1, b:0),
% 1.23/1.64 'class_OrderedGroup_Ocancel__semigroup__add' [181, 1] (w:1, o:171, a:
% 1.23/1.64 1, s:1, b:0),
% 1.23/1.64 'c_Relation_Ototal__on' [183, 3] (w:1, o:251, a:1, s:1, b:0),
% 1.23/1.64 'class_Orderings_Otop' [185, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Omult__mono' [186, 1] (w:1, o:107, a:1, s:1
% 1.23/1.64 , b:0),
% 1.23/1.64 'class_Ring__and__Field_Omult__mono1' [187, 1] (w:1, o:108, a:1, s:1
% 1.23/1.64 , b:0),
% 1.23/1.64 'class_Finite__Set_Ofinite_Ofinite' [188, 1] (w:1, o:184, a:1, s:1
% 1.23/1.64 , b:0),
% 1.23/1.64 'class_Orderings_Opreorder' [189, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.23/1.64 'c_Wellfounded_Oacc' [195, 2] (w:1, o:226, a:1, s:1, b:0),
% 1.23/1.64 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1' [197, 3]
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% 28.95/29.31 Deletedinuse: 1
% 28.95/29.31
% 28.95/29.31 Resimplifying inuse:
% 28.95/29.31 Done
% 28.95/29.31
% 28.95/29.31 Resimplifying inuse:
% 28.95/29.31 Done
% 28.95/29.31
% 28.95/29.31 Resimplifying clauses:
% 28.95/29.31 Done
% 28.95/29.31
% 28.95/29.31
% 28.95/29.31 Intermediate Status:
% 28.95/29.31 Generated: 165147
% 28.95/29.31 Kept: 43540
% 28.95/29.31 Inuse: 760
% 28.95/29.31 Deleted: 185
% 28.95/29.31 Deletedinuse: 1
% 28.95/29.31
% 28.95/29.31 Resimplifying inuse:
% 28.95/29.31 Done
% 28.95/29.31
% 28.95/29.31 Resimplifying inuse:
% 28.95/29.31 Done
% 28.95/29.31
% 28.95/29.31
% 28.95/29.31 Intermediate Status:
% 28.95/29.31 Generated: 171568
% 28.95/29.31 Kept: 45569
% 28.95/29.31 Inuse: 779
% 28.95/29.31 Deleted: 223
% 28.95/29.31 Deletedinuse: 2
% 28.95/29.31
% 28.95/29.31 Resimplifying inuse:
% 28.95/29.31 Done
% 28.95/29.31
% 28.95/29.31
% 28.95/29.31 Intermediate Status:
% 28.95/29.31 Generated: 179960
% 28.95/29.31 Kept: 48780
% 28.95/29.31 Inuse: 800
% 28.95/29.31 Deleted: 223
% 28.95/29.31 Deletedinuse: 2
% 28.95/29.31
% 28.95/29.31 Resimplifying inuse:
% 28.95/29.31 Done
% 28.95/29.31
% 28.95/29.31 Resimplifying inuse:
% 28.95/29.31 Done
% 28.95/29.31
% 28.95/29.31
% 28.95/29.31 Intermediate Status:
% 70.71/71.16 Generated: 193749
% 70.71/71.16 Kept: 50934
% 70.71/71.16 Inuse: 843
% 70.71/71.16 Deleted: 231
% 70.71/71.16 Deletedinuse: 10
% 70.71/71.16
% 70.71/71.16 Resimplifying inuse:
% 70.71/71.16 Done
% 70.71/71.16
% 70.71/71.16 Resimplifying inuse:
% 70.71/71.16 Done
% 70.71/71.16
% 70.71/71.16
% 70.71/71.16 Intermediate Status:
% 70.71/71.16 Generated: 212739
% 70.71/71.16 Kept: 55483
% 70.71/71.16 Inuse: 863
% 70.71/71.16 Deleted: 231
% 70.71/71.16 Deletedinuse: 10
% 70.71/71.16
% 70.71/71.16 Resimplifying inuse:
% 70.71/71.16 Done
% 70.71/71.16
% 70.71/71.16 Resimplifying inuse:
% 70.71/71.16 Done
% 70.71/71.16
% 70.71/71.16
% 70.71/71.16 Intermediate Status:
% 70.71/71.16 Generated: 222118
% 70.71/71.16 Kept: 57588
% 70.71/71.16 Inuse: 898
% 70.71/71.16 Deleted: 231
% 70.71/71.16 Deletedinuse: 10
% 70.71/71.16
% 70.71/71.16 Resimplifying inuse:
% 70.71/71.16 Done
% 70.71/71.16
% 70.71/71.16 Resimplifying inuse:
% 70.71/71.16 Done
% 70.71/71.16
% 70.71/71.16
% 70.71/71.16 Intermediate Status:
% 70.71/71.16 Generated: 228531
% 70.71/71.16 Kept: 59599
% 70.71/71.16 Inuse: 916
% 70.71/71.16 Deleted: 231
% 70.71/71.16 Deletedinuse: 10
% 70.71/71.16
% 70.71/71.16 Resimplifying inuse:
% 70.71/71.16 Done
% 70.71/71.16
% 70.71/71.16 Resimplifying inuse:
% 70.71/71.16 Done
% 70.71/71.16
% 70.71/71.16
% 70.71/71.16 Intermediate Status:
% 70.71/71.16 Generated: 244034
% 70.71/71.16 Kept: 63262
% 70.71/71.16 Inuse: 938
% 70.71/71.16 Deleted: 231
% 70.71/71.16 Deletedinuse: 10
% 70.71/71.16
% 70.71/71.16 Resimplifying inuse:
% 70.71/71.16 Done
% 70.71/71.16
% 70.71/71.16 Resimplifying clauses:
% 70.71/71.16 Done
% 70.71/71.16
% 70.71/71.16 Resimplifying inuse:
% 70.71/71.16 Done
% 70.71/71.16
% 70.71/71.16
% 70.71/71.16 Intermediate Status:
% 70.71/71.16 Generated: 263436
% 70.71/71.16 Kept: 66787
% 70.71/71.16 Inuse: 993
% 70.71/71.16 Deleted: 631
% 70.71/71.16 Deletedinuse: 10
% 70.71/71.16
% 70.71/71.16 Resimplifying inuse:
% 70.71/71.16 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 270988
% 70.71/71.17 Kept: 68917
% 70.71/71.17 Inuse: 1018
% 70.71/71.17 Deleted: 631
% 70.71/71.17 Deletedinuse: 10
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 279668
% 70.71/71.17 Kept: 71012
% 70.71/71.17 Inuse: 1045
% 70.71/71.17 Deleted: 635
% 70.71/71.17 Deletedinuse: 13
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 286323
% 70.71/71.17 Kept: 73143
% 70.71/71.17 Inuse: 1061
% 70.71/71.17 Deleted: 635
% 70.71/71.17 Deletedinuse: 13
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 292490
% 70.71/71.17 Kept: 75225
% 70.71/71.17 Inuse: 1077
% 70.71/71.17 Deleted: 635
% 70.71/71.17 Deletedinuse: 13
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 309215
% 70.71/71.17 Kept: 77537
% 70.71/71.17 Inuse: 1102
% 70.71/71.17 Deleted: 635
% 70.71/71.17 Deletedinuse: 13
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 316636
% 70.71/71.17 Kept: 79875
% 70.71/71.17 Inuse: 1117
% 70.71/71.17 Deleted: 635
% 70.71/71.17 Deletedinuse: 13
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 323871
% 70.71/71.17 Kept: 81895
% 70.71/71.17 Inuse: 1131
% 70.71/71.17 Deleted: 635
% 70.71/71.17 Deletedinuse: 13
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying clauses:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 330998
% 70.71/71.17 Kept: 83938
% 70.71/71.17 Inuse: 1147
% 70.71/71.17 Deleted: 820
% 70.71/71.17 Deletedinuse: 13
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 339766
% 70.71/71.17 Kept: 85940
% 70.71/71.17 Inuse: 1169
% 70.71/71.17 Deleted: 820
% 70.71/71.17 Deletedinuse: 13
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 353636
% 70.71/71.17 Kept: 89445
% 70.71/71.17 Inuse: 1172
% 70.71/71.17 Deleted: 820
% 70.71/71.17 Deletedinuse: 13
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 362964
% 70.71/71.17 Kept: 91817
% 70.71/71.17 Inuse: 1192
% 70.71/71.17 Deleted: 820
% 70.71/71.17 Deletedinuse: 13
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 380549
% 70.71/71.17 Kept: 95546
% 70.71/71.17 Inuse: 1235
% 70.71/71.17 Deleted: 822
% 70.71/71.17 Deletedinuse: 13
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 407934
% 70.71/71.17 Kept: 99066
% 70.71/71.17 Inuse: 1245
% 70.71/71.17 Deleted: 827
% 70.71/71.17 Deletedinuse: 18
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 423201
% 70.71/71.17 Kept: 101072
% 70.71/71.17 Inuse: 1253
% 70.71/71.17 Deleted: 832
% 70.71/71.17 Deletedinuse: 21
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 449268
% 70.71/71.17 Kept: 103265
% 70.71/71.17 Inuse: 1261
% 70.71/71.17 Deleted: 834
% 70.71/71.17 Deletedinuse: 21
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 464942
% 70.71/71.17 Kept: 105354
% 70.71/71.17 Inuse: 1266
% 70.71/71.17 Deleted: 840
% 70.71/71.17 Deletedinuse: 27
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying clauses:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 486340
% 70.71/71.17 Kept: 109292
% 70.71/71.17 Inuse: 1273
% 70.71/71.17 Deleted: 1067
% 70.71/71.17 Deletedinuse: 38
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 70.71/71.17 Generated: 498851
% 70.71/71.17 Kept: 111460
% 70.71/71.17 Inuse: 1303
% 70.71/71.17 Deleted: 1082
% 70.71/71.17 Deletedinuse: 45
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17 Resimplifying inuse:
% 70.71/71.17 Done
% 70.71/71.17
% 70.71/71.17
% 70.71/71.17 Intermediate Status:
% 124.97/125.41 Generated: 514016
% 124.97/125.41 Kept: 113516
% 124.97/125.41 Inuse: 1338
% 124.97/125.41 Deleted: 1083
% 124.97/125.41 Deletedinuse: 46
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 575064
% 124.97/125.41 Kept: 122000
% 124.97/125.41 Inuse: 1353
% 124.97/125.41 Deleted: 1083
% 124.97/125.41 Deletedinuse: 46
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 629184
% 124.97/125.41 Kept: 129145
% 124.97/125.41 Inuse: 1358
% 124.97/125.41 Deleted: 1083
% 124.97/125.41 Deletedinuse: 46
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying clauses:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 644949
% 124.97/125.41 Kept: 132716
% 124.97/125.41 Inuse: 1379
% 124.97/125.41 Deleted: 1319
% 124.97/125.41 Deletedinuse: 46
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 659454
% 124.97/125.41 Kept: 135356
% 124.97/125.41 Inuse: 1403
% 124.97/125.41 Deleted: 1319
% 124.97/125.41 Deletedinuse: 46
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 673657
% 124.97/125.41 Kept: 137752
% 124.97/125.41 Inuse: 1428
% 124.97/125.41 Deleted: 1319
% 124.97/125.41 Deletedinuse: 46
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 691613
% 124.97/125.41 Kept: 141068
% 124.97/125.41 Inuse: 1443
% 124.97/125.41 Deleted: 1319
% 124.97/125.41 Deletedinuse: 46
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 705558
% 124.97/125.41 Kept: 143841
% 124.97/125.41 Inuse: 1458
% 124.97/125.41 Deleted: 1320
% 124.97/125.41 Deletedinuse: 47
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 715044
% 124.97/125.41 Kept: 145969
% 124.97/125.41 Inuse: 1463
% 124.97/125.41 Deleted: 1320
% 124.97/125.41 Deletedinuse: 47
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 738601
% 124.97/125.41 Kept: 148721
% 124.97/125.41 Inuse: 1474
% 124.97/125.41 Deleted: 1331
% 124.97/125.41 Deletedinuse: 49
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying clauses:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 754976
% 124.97/125.41 Kept: 150831
% 124.97/125.41 Inuse: 1498
% 124.97/125.41 Deleted: 1565
% 124.97/125.41 Deletedinuse: 50
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 773691
% 124.97/125.41 Kept: 153086
% 124.97/125.41 Inuse: 1532
% 124.97/125.41 Deleted: 1567
% 124.97/125.41 Deletedinuse: 51
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 783113
% 124.97/125.41 Kept: 155330
% 124.97/125.41 Inuse: 1547
% 124.97/125.41 Deleted: 1567
% 124.97/125.41 Deletedinuse: 51
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 796647
% 124.97/125.41 Kept: 158289
% 124.97/125.41 Inuse: 1561
% 124.97/125.41 Deleted: 1568
% 124.97/125.41 Deletedinuse: 51
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 815174
% 124.97/125.41 Kept: 160486
% 124.97/125.41 Inuse: 1564
% 124.97/125.41 Deleted: 1587
% 124.97/125.41 Deletedinuse: 68
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 826339
% 124.97/125.41 Kept: 163264
% 124.97/125.41 Inuse: 1573
% 124.97/125.41 Deleted: 1588
% 124.97/125.41 Deletedinuse: 68
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 848255
% 124.97/125.41 Kept: 168350
% 124.97/125.41 Inuse: 1583
% 124.97/125.41 Deleted: 1597
% 124.97/125.41 Deletedinuse: 77
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 865912
% 124.97/125.41 Kept: 172596
% 124.97/125.41 Inuse: 1588
% 124.97/125.41 Deleted: 1597
% 124.97/125.41 Deletedinuse: 77
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying clauses:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 877933
% 124.97/125.41 Kept: 175336
% 124.97/125.41 Inuse: 1593
% 124.97/125.41 Deleted: 2080
% 124.97/125.41 Deletedinuse: 77
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 890074
% 124.97/125.41 Kept: 178092
% 124.97/125.41 Inuse: 1598
% 124.97/125.41 Deleted: 2080
% 124.97/125.41 Deletedinuse: 77
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 909114
% 124.97/125.41 Kept: 180646
% 124.97/125.41 Inuse: 1633
% 124.97/125.41 Deleted: 2080
% 124.97/125.41 Deletedinuse: 77
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 924036
% 124.97/125.41 Kept: 183008
% 124.97/125.41 Inuse: 1653
% 124.97/125.41 Deleted: 2080
% 124.97/125.41 Deletedinuse: 77
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 939535
% 124.97/125.41 Kept: 185206
% 124.97/125.41 Inuse: 1678
% 124.97/125.41 Deleted: 2080
% 124.97/125.41 Deletedinuse: 77
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 960581
% 124.97/125.41 Kept: 187530
% 124.97/125.41 Inuse: 1683
% 124.97/125.41 Deleted: 2080
% 124.97/125.41 Deletedinuse: 77
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 969357
% 124.97/125.41 Kept: 189546
% 124.97/125.41 Inuse: 1684
% 124.97/125.41 Deleted: 2080
% 124.97/125.41 Deletedinuse: 77
% 124.97/125.41
% 124.97/125.41 Resimplifying inuse:
% 124.97/125.41 Done
% 124.97/125.41
% 124.97/125.41
% 124.97/125.41 Intermediate Status:
% 124.97/125.41 Generated: 990041
% 231.92/232.41 Kept: 191865
% 231.92/232.41 Inuse: 1688
% 231.92/232.41 Deleted: 2080
% 231.92/232.41 Deletedinuse: 77
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1010467
% 231.92/232.41 Kept: 194227
% 231.92/232.41 Inuse: 1693
% 231.92/232.41 Deleted: 2080
% 231.92/232.41 Deletedinuse: 77
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41 Resimplifying clauses:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1030671
% 231.92/232.41 Kept: 196586
% 231.92/232.41 Inuse: 1698
% 231.92/232.41 Deleted: 2223
% 231.92/232.41 Deletedinuse: 78
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1046418
% 231.92/232.41 Kept: 199010
% 231.92/232.41 Inuse: 1723
% 231.92/232.41 Deleted: 2223
% 231.92/232.41 Deletedinuse: 78
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1059063
% 231.92/232.41 Kept: 201038
% 231.92/232.41 Inuse: 1738
% 231.92/232.41 Deleted: 2223
% 231.92/232.41 Deletedinuse: 78
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1076475
% 231.92/232.41 Kept: 204276
% 231.92/232.41 Inuse: 1753
% 231.92/232.41 Deleted: 2223
% 231.92/232.41 Deletedinuse: 78
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1088194
% 231.92/232.41 Kept: 206623
% 231.92/232.41 Inuse: 1758
% 231.92/232.41 Deleted: 2223
% 231.92/232.41 Deletedinuse: 78
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1099599
% 231.92/232.41 Kept: 209198
% 231.92/232.41 Inuse: 1763
% 231.92/232.41 Deleted: 2223
% 231.92/232.41 Deletedinuse: 78
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1111012
% 231.92/232.41 Kept: 211769
% 231.92/232.41 Inuse: 1768
% 231.92/232.41 Deleted: 2223
% 231.92/232.41 Deletedinuse: 78
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1124012
% 231.92/232.41 Kept: 214229
% 231.92/232.41 Inuse: 1773
% 231.92/232.41 Deleted: 2223
% 231.92/232.41 Deletedinuse: 78
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41 Resimplifying clauses:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1136086
% 231.92/232.41 Kept: 216249
% 231.92/232.41 Inuse: 1796
% 231.92/232.41 Deleted: 2360
% 231.92/232.41 Deletedinuse: 79
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1158018
% 231.92/232.41 Kept: 219349
% 231.92/232.41 Inuse: 1817
% 231.92/232.41 Deleted: 2360
% 231.92/232.41 Deletedinuse: 79
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1181624
% 231.92/232.41 Kept: 221377
% 231.92/232.41 Inuse: 1839
% 231.92/232.41 Deleted: 2360
% 231.92/232.41 Deletedinuse: 79
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1201368
% 231.92/232.41 Kept: 225917
% 231.92/232.41 Inuse: 1848
% 231.92/232.41 Deleted: 2360
% 231.92/232.41 Deletedinuse: 79
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1218186
% 231.92/232.41 Kept: 228923
% 231.92/232.41 Inuse: 1858
% 231.92/232.41 Deleted: 2360
% 231.92/232.41 Deletedinuse: 79
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1232891
% 231.92/232.41 Kept: 231549
% 231.92/232.41 Inuse: 1863
% 231.92/232.41 Deleted: 2360
% 231.92/232.41 Deletedinuse: 79
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1250632
% 231.92/232.41 Kept: 234211
% 231.92/232.41 Inuse: 1888
% 231.92/232.41 Deleted: 2360
% 231.92/232.41 Deletedinuse: 79
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41 Resimplifying clauses:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1269705
% 231.92/232.41 Kept: 236612
% 231.92/232.41 Inuse: 1896
% 231.92/232.41 Deleted: 2657
% 231.92/232.41 Deletedinuse: 84
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1292184
% 231.92/232.41 Kept: 238716
% 231.92/232.41 Inuse: 1903
% 231.92/232.41 Deleted: 2657
% 231.92/232.41 Deletedinuse: 84
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1306604
% 231.92/232.41 Kept: 240726
% 231.92/232.41 Inuse: 1920
% 231.92/232.41 Deleted: 2657
% 231.92/232.41 Deletedinuse: 84
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1323114
% 231.92/232.41 Kept: 243062
% 231.92/232.41 Inuse: 1943
% 231.92/232.41 Deleted: 2663
% 231.92/232.41 Deletedinuse: 90
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1336596
% 231.92/232.41 Kept: 245179
% 231.92/232.41 Inuse: 1968
% 231.92/232.41 Deleted: 2663
% 231.92/232.41 Deletedinuse: 90
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1350484
% 231.92/232.41 Kept: 247188
% 231.92/232.41 Inuse: 1993
% 231.92/232.41 Deleted: 2663
% 231.92/232.41 Deletedinuse: 90
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1370430
% 231.92/232.41 Kept: 250464
% 231.92/232.41 Inuse: 2003
% 231.92/232.41 Deleted: 2663
% 231.92/232.41 Deletedinuse: 90
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 1381092
% 231.92/232.41 Kept: 252611
% 231.92/232.41 Inuse: 2018
% 231.92/232.41 Deleted: 2663
% 231.92/232.41 Deletedinuse: 90
% 231.92/232.41
% 231.92/232.41 Resimplifying inuse:
% 231.92/232.41 Done
% 231.92/232.41
% 231.92/232.41
% 231.92/232.41 Intermediate Status:
% 231.92/232.41 Generated: 13943Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------