%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SCT094-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n008.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 21:01:10 EDT 2022
% Result : Unsatisfiable 1.39s 1.81s
% Output : Refutation 1.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT094-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Jul 2 04:59:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.36/1.77 *** allocated 10000 integers for termspace/termends
% 1.36/1.77 *** allocated 10000 integers for clauses
% 1.36/1.77 *** allocated 10000 integers for justifications
% 1.36/1.77 *** allocated 15000 integers for termspace/termends
% 1.36/1.77 *** allocated 22500 integers for termspace/termends
% 1.36/1.77 *** allocated 33750 integers for termspace/termends
% 1.36/1.77 *** allocated 50625 integers for termspace/termends
% 1.36/1.77 Bliksem 1.12
% 1.36/1.77
% 1.36/1.77
% 1.36/1.77 Automatic Strategy Selection
% 1.36/1.77
% 1.36/1.77 Clauses:
% 1.36/1.77 [
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.36/1.77 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.36/1.77 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.36/1.77 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.36/1.77 ) ],
% 1.36/1.77 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.36/1.77 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.36/1.77 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.36/1.77 ) ) ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.36/1.77 'c_Orderings_Obot__class_Obot'( X ), Y, X ),
% 1.36/1.77 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.36/1.77 'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'(
% 1.36/1.77 X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.36/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.36/1.77 ), X ) ],
% 1.36/1.77 [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.36/1.77 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.36/1.77 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.36/1.77 'tc_bool' ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.36/1.77 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.36/1.77 ,
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.36/1.77 ), X ) ) ],
% 1.36/1.77 [ 'c_Relation_Osym'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 1.36/1.77 , 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Osym'(
% 1.36/1.77 Y, Z ) ), ~( 'c_Relation_Osym'( X, Z ) ) ],
% 1.36/1.77 [ =( 'c_Relation_ODomain'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, T ), U,
% 1.36/1.77 'tc_prod'( Z, T ) ), Z, T ), 'c_Set_Oinsert'( X, 'c_Relation_ODomain'( U
% 1.36/1.77 , Z, T ), Z ) ) ],
% 1.36/1.77 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.36/1.77 ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.36/1.77 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( X
% 1.36/1.77 , 'tc_bool' ) ) ],
% 1.36/1.77 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( 'c_Set_Oinsert'( Z,
% 1.36/1.77 X, T ), Y ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~(
% 1.36/1.77 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Z ), T ) ), W ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.36/1.77 ), W, X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.36/1.77 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~(
% 1.36/1.77 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Z ), U ) ), W ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W
% 1.36/1.77 ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.36/1.77 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.36/1.77 Y, T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.36/1.77 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.36/1.77 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.36/1.77 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.36/1.77 'c_Set_Oinsert'( X, Y, Z ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ) ],
% 1.36/1.77 [ =( 'c_Relation_OImage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.36/1.77 , 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.36/1.77 'tc_bool' ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.36/1.77 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.36/1.77 , Z, X ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.36/1.77 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.36/1.77 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.36/1.77 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.36/1.77 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.36/1.77 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.36/1.77 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.36/1.77 , Z ), 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.36/1.77 'c_Set_Oinsert'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.36/1.77 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 1.36/1.77 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 1.36/1.77 'c_Set_Oinsert'( hAPP( Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.36/1.77 T, 'tc_bool' ) ), T ), X, T ) ) ) ],
% 1.36/1.77 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.36/1.77 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 1.36/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.36/1.77 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.36/1.77 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.36/1.77 ) ],
% 1.36/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.36/1.77 X, 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool'
% 1.36/1.77 ) ) ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 'c_Orderings_Otop__class_Otop'( X ), Y, X ),
% 1.36/1.77 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.36/1.77 'c_Orderings_Otop__class_Otop'( X ), X ), 'c_Orderings_Otop__class_Otop'(
% 1.36/1.77 X ) ) ],
% 1.36/1.77 [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.36/1.77 'tc_bool' ) ), Z, Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 1.36/1.77 'tc_bool' ) ) ) ],
% 1.36/1.77 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.36/1.77 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 1.36/1.77 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.36/1.77 ) ), Y, 'tc_fun'( X, 'tc_bool' ) ) ],
% 1.36/1.77 [ ~( =( hAPP( hAPP( 'c_Finite__Set_Osetsum'( X, 'tc_nat' ), Y ), Z ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z
% 1.36/1.77 , X ) ), =( hAPP( Y, T ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.36/1.77 hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Z ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ) ), U ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), T ), Z ) ), U ) ) ],
% 1.36/1.77 [ 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.36/1.77 'tc_bool' ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.36/1.77 'tc_bool' ) ), Z ), 'tc_fun'( X, 'tc_bool' ) ), ~( 'c_lessequals'( Z, Y,
% 1.36/1.77 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.36/1.77 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.36/1.77 hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Z, 'tc_bool' ) ), Y ),
% 1.36/1.77 hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Z, 'tc_bool' ) ), X ),
% 1.36/1.77 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.36/1.77 [ 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.36/1.77 'tc_bool' ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.36/1.77 'tc_bool' ) ), Z ), 'tc_fun'( X, 'tc_bool' ) ), ~( 'c_lessequals'( Z, Y,
% 1.36/1.77 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.36/1.77 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_lessequals'( Z, Y, X
% 1.36/1.77 ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.36/1.77 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y,
% 1.36/1.77 X ), Z ), 'c_Lattices_Oupper__semilattice__class_Osup'( T, U, 'tc_fun'( Y
% 1.36/1.77 , 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( T, U, 'tc_fun'( Y,
% 1.36/1.77 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.36/1.77 hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ) ), hAPP( hAPP(
% 1.36/1.77 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'(
% 1.36/1.77 U, Y ) ), ~( 'c_Finite__Set_Ofinite'( T, Y ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.36/1.77 'c_HOL_Oone__class_Oone'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.36/1.77 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.36/1.77 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ),
% 1.36/1.77 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.36/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Set_Oinsert'( Y
% 1.36/1.77 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.36/1.77 'tc_bool' ) ), T ) ) ],
% 1.36/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X, Y
% 1.36/1.77 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.36/1.77 'tc_bool' ) ), Z ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.36/1.77 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.36/1.77 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.36/1.77 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~(
% 1.36/1.77 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.36/1.77 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.36/1.77 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.36/1.77 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'(
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 1.36/1.77 Y, Y ), 'tc_bool' ) ), Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ]
% 1.36/1.77 ,
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~(
% 1.36/1.77 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.36/1.77 'c_lessequals'( Z, T, X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~(
% 1.36/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.36/1.77 'c_lessequals'( T, Z, X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.36/1.77 ) ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.36/1.77 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.36/1.77 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.36/1.77 ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.36/1.77 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.36/1.77 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.36/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.36/1.77 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.36/1.77 ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.36/1.77 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.36/1.77 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.36/1.77 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.36/1.77 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.36/1.77 ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.36/1.77 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.36/1.77 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.36/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.36/1.77 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.36/1.77 ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.36/1.77 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.36/1.77 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.36/1.77 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.36/1.77 ,
% 1.36/1.77 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, X, Z ), 'tc_fun'( Z, 'tc_bool'
% 1.36/1.77 ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.36/1.77 'c_Power_Opower__class_Opower'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.36/1.77 , Y ), Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.36/1.77 'c_Power_Opower__class_Opower'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.36/1.77 , 'c_HOL_Oone__class_Oone'( X ) ), Z, X ) ),
% 1.36/1.77 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.36/1.77 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 1.36/1.77 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.36/1.77 ) ],
% 1.36/1.77 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'(
% 1.36/1.77 'c_Set_Oinsert'( Z, X, Y ), Y ) ) ],
% 1.36/1.77 [ 'c_Finite__Set_Ofinite'( 'c_Set_Oinsert'( X, Y, Z ), Z ), ~(
% 1.36/1.77 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.36/1.77 [ 'c_Finite__Set_Ofinite'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.36/1.77 'tc_bool' ) ), X ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.36/1.77 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.36/1.77 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~( hBOOL(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.36/1.77 ) ), T ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), Z, X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( hBOOL(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.36/1.77 ) ), Z ) ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~( hBOOL( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.36/1.77 Z ) ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( hBOOL(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.36/1.77 ) ), T ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.36/1.77 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.36/1.77 ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.36/1.77 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.36/1.77 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.36/1.77 Z, X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 1.36/1.77 ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), T ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.36/1.77 ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 1.36/1.77 ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), T ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.36/1.77 ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y, hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), =( Y, Z ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.36/1.77 X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.36/1.77 X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.36/1.77 , Y ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.36/1.77 X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.36/1.77 X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.36/1.77 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ), X ), ~(
% 1.36/1.77 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.36/1.77 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.36/1.77 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( Y, Z )
% 1.36/1.77 ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ) ],
% 1.36/1.77 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( Y, Z )
% 1.36/1.77 ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( Y, Z,
% 1.36/1.77 X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.36/1.77 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ],
% 1.36/1.77 [ 'c_lessequals'( 'c_Relation_OImage'( X,
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.36/1.77 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.36/1.77 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 1.36/1.77 'tc_fun'( U, 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ) ],
% 1.36/1.77 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.36/1.77 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.36/1.77 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ), 'c_lessequals'( T, X,
% 1.36/1.77 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.36/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.36/1.77 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.36/1.77 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( T, X,
% 1.36/1.77 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.36/1.77 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ),
% 1.36/1.77 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Finite__Set_Osetprod'( Y, Z, T
% 1.36/1.77 , X ), 'c_Finite__Set_Osetprod'( Y, U, T, X ), X ), ~( 'c_lessequals'( Z
% 1.36/1.77 , U, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ) ]
% 1.36/1.77 ,
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.36/1.77 X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.36/1.77 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ), Y ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.36/1.77 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Y ) ) ), hBOOL( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.36/1.77 Z ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.36/1.77 T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Y ) ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.36/1.77 ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.36/1.77 T ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.36/1.77 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.36/1.77 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.36/1.77 ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.36/1.77 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.36/1.77 ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.36/1.77 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), T ) ), Z ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.36/1.77 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.36/1.77 Y ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.36/1.77 ) ) ],
% 1.36/1.77 [ 'c_lessequals'( 'c_Finite__Set_Ocard'( X, Y ), 'c_Finite__Set_Ocard'(
% 1.36/1.77 'c_Set_Oinsert'( Z, X, Y ), Y ), 'tc_nat' ), ~( 'c_Finite__Set_Ofinite'(
% 1.36/1.77 X, Y ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.36/1.77 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ),
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W
% 1.36/1.77 ) ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W
% 1.36/1.77 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), T ), U ) ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.36/1.77 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ),
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.36/1.77 ) ), W ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.36/1.77 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ) ), W ) ), ~(
% 1.36/1.77 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), T ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.36/1.77 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) )
% 1.36/1.77 ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ), ~( 'c_Finite__Set_Ofinite'( Y
% 1.36/1.77 , T ) ), =( hAPP( hAPP( 'c_Finite__Set_Osetsum'( T, X ), U ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.36/1.77 'tc_bool' ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_Finite__Set_Osetsum'( T, X ), U ), Y ) ), hAPP( hAPP(
% 1.36/1.77 'c_Finite__Set_Osetsum'( T, X ), U ), Z ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.36/1.77 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.36/1.77 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.36/1.77 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.36/1.77 ), Y ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( Y, T, X )
% 1.36/1.77 ), 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ) ],
% 1.36/1.77 [ 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.36/1.77 Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_lessequals'(
% 1.36/1.77 'c_Relation_Orel__comp'( X, Y, Z, Z, Z ), X, 'tc_fun'( 'tc_prod'( Z, Z )
% 1.36/1.77 , 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Y, Z ) ), ~(
% 1.36/1.77 'c_Wellfounded_Owf'( X, Z ) ) ],
% 1.36/1.77 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL( hAPP(
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 1.36/1.77 'tc_bool' ) ), Y ) ) ) ],
% 1.36/1.77 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.36/1.77 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ],
% 1.36/1.77 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.36/1.77 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 1.36/1.77 [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.36/1.77 'c_Relation_ODomain'( X, Y, Y ), 'c_Relation_ORange'( Z, Y, Y ), 'tc_fun'(
% 1.36/1.77 Y, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool'
% 1.36/1.77 ) ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ), ~( 'c_Wellfounded_Owf'( X, Y
% 1.36/1.77 ) ), 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.36/1.77 ) ) ), =( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.36/1.77 ) ) ), =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ],
% 1.36/1.77 [ 'c_Relation_Osingle__valued'( 'c_Relation_Orel__comp'( X, Y, Z, T, U )
% 1.36/1.77 , Z, U ), ~( 'c_Relation_Osingle__valued'( Y, T, U ) ), ~(
% 1.36/1.77 'c_Relation_Osingle__valued'( X, Z, T ) ) ],
% 1.36/1.77 [ 'c_Relation_Orefl__on'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 X, Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( T, U, 'tc_fun'( 'tc_prod'(
% 1.36/1.77 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Orefl__on'( Y, U, Z ) ), ~(
% 1.36/1.77 'c_Relation_Orefl__on'( X, T, Z ) ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.36/1.77 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.36/1.77 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.36/1.77 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.36/1.77 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.36/1.77 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.36/1.77 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.36/1.77 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Finite__Set_Ocard'(
% 1.36/1.77 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ), ~(
% 1.36/1.77 'c_Finite__Set_Ofinite'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.36/1.77 'tc_bool' ) ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.36/1.77 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( hBOOL(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.36/1.77 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( hBOOL(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.36/1.77 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.36/1.77 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.36/1.77 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.36/1.77 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.36/1.77 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'(
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( Y,
% 1.36/1.77 'tc_bool' ) ), Y ) ) ],
% 1.36/1.77 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'(
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( Y,
% 1.36/1.77 'tc_bool' ) ), Y ) ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.36/1.77 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 'c_Orderings_Obot__class_Obot'( X ), Y, X ), Y ) ],
% 1.36/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.36/1.77 X, 'tc_bool' ) ), Y ) ],
% 1.36/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.36/1.77 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.36/1.77 'tc_bool' ) ), X ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.36/1.77 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( Y,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.36/1.77 X ) ) ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.36/1.77 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.36/1.77 [ 'c_Relation_Orefl__on'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.36/1.77 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.36/1.77 'c_Relation_OId'( X ), 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' ) ), X ) ]
% 1.36/1.77 ,
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.36/1.77 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.36/1.77 ],
% 1.36/1.77 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.36/1.77 'c_Orderings_Otop__class_Otop'( X ) ) ), =( Z,
% 1.36/1.77 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.36/1.77 'c_Orderings_Otop__class_Otop'( X ) ) ), =( Y,
% 1.36/1.77 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.36/1.77 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.36/1.77 , X ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.36/1.77 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.36/1.77 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.36/1.77 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.36/1.77 ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.36/1.77 ~( 'c_lessequals'( X, 'c_Relation_OImage'( Z, X, Y, Y ), 'tc_fun'( Y,
% 1.36/1.77 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.36/1.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.36/1.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Y,
% 1.36/1.77 'tc_fun'( X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.36/1.77 'tc_bool' ) ) ) ],
% 1.36/1.77 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), X ), 'tc_fun'(
% 1.36/1.77 Y, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool'
% 1.36/1.77 ) ) ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.36/1.77 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.36/1.77 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.36/1.77 Y ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.36/1.77 Y ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.36/1.77 Y ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.36/1.77 Y ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.36/1.77 Y ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.36/1.77 Y ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.36/1.77 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( 'c_lessequals'( Y, T, X
% 1.36/1.77 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.36/1.77 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.36/1.77 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.36/1.77 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ],
% 1.36/1.77 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.36/1.77 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1'( X, Z, T ) ) ) ),
% 1.36/1.77 ~( 'c_Wellfounded_Owf'( Z, T ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), U ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), U ) )
% 1.36/1.77 ), ~( 'c_lessequals'( Y, T, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.36/1.77 ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.36/1.77 'c_Power_Opower__class_Opower'( Y, Z, X ) ),
% 1.36/1.77 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.36/1.77 ), Z, X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.36/1.77 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.36/1.77 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), hAPP(
% 1.36/1.77 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.36/1.77 hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), hAPP(
% 1.36/1.77 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ), X ), ~( 'c_lessequals'( Y
% 1.36/1.77 , Z, 'tc_nat' ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Z,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.36/1.77 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.36/1.77 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.36/1.77 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.36/1.77 ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.36/1.77 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.77 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.36/1.77 ) ) ],
% 1.36/1.77 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.36/1.77 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.36/1.77 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_Set_Oinsert'( T, X, Z ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.36/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.36/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.36/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.36/1.77 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.36/1.77 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.36/1.77 ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.36/1.77 X ), Y ), Z ) ), Z ), Y ) ],
% 1.36/1.77 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), 'c_Set_Oinsert'( Y
% 1.36/1.77 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ) ]
% 1.36/1.77 ,
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.36/1.77 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.36/1.77 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.36/1.77 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.36/1.77 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 1.36/1.77 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.36/1.77 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.36/1.77 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.36/1.77 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 1.36/1.77 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 1.36/1.77 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.36/1.77 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.36/1.77 ,
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.36/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.36/1.77 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.36/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.36/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X, 'tc_fun'( Y,
% 1.36/1.77 'tc_bool' ) ), X ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ],
% 1.36/1.77 [ 'c_lessequals'( 'c_Relation_Orel__comp'( X, Y, Z, T, U ),
% 1.36/1.77 'c_Relation_Orel__comp'( W, V0, Z, T, U ), 'tc_fun'( 'tc_prod'( Z, U ),
% 1.36/1.77 'tc_bool' ) ), ~( 'c_lessequals'( Y, V0, 'tc_fun'( 'tc_prod'( T, U ),
% 1.36/1.77 'tc_bool' ) ) ), ~( 'c_lessequals'( X, W, 'tc_fun'( 'tc_prod'( Z, T ),
% 1.36/1.77 'tc_bool' ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.36/1.77 'c_HOL_Osgn__class_Osgn'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.36/1.77 ), 'c_HOL_Oone__class_Oone'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.36/1.77 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.36/1.77 X ), Y ), Z ) ), T ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.36/1.77 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.36/1.77 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.36/1.77 X ), Y ), Z ) ), T ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.36/1.77 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.36/1.77 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.36/1.77 [ =( 'c_Relation_OImage'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 X, Y, 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ), U, Z, T ),
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_OImage'( X, U,
% 1.36/1.77 Z, T ), 'c_Relation_OImage'( Y, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ) ]
% 1.36/1.77 ,
% 1.36/1.77 [ =( 'c_Relation_OImage'( X,
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.36/1.77 'tc_bool' ) ), T, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.77 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 1.36/1.77 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.36/1.77 ), Y ) ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.36/1.77 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.36/1.77 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1'( X, Z, T ) ) ) ), ~(
% 1.36/1.77 'c_Wellfounded_Owf'( Z, T ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.36/1.77 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.36/1.77 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.36/1.77 [ 'c_lessequals'( 'c_Relation_OImage'( X, Y, Z, T ), U, 'tc_fun'( T,
% 1.36/1.77 'tc_bool' ) ), ~( 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.36/1.77 'tc_fun'( Z, 'tc_bool' ) ), 'c_Relation_OImage'( 'c_Relation_Oconverse'(
% 1.36/1.77 X, Z, T ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( T, 'tc_bool' )
% 1.36/1.77 ), U ), T, Z ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.36/1.77 [ 'c_lessequals'( X, hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y,
% 1.36/1.77 'tc_bool' ) ), 'c_Relation_OImage'( 'c_Relation_Oconverse'( Z, Y, T ),
% 1.36/1.77 hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( T, 'tc_bool' ) ), U ), T
% 1.36/1.77 , Y ) ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_Relation_OImage'( Z, X, Y, T ), U, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.36/1.77 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 1.36/1.77 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.36/1.77 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.36/1.77 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.36/1.77 [ 'c_Relation_Osingle__valued'( 'c_Relation_OId'( X ), X, X ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.36/1.77 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.36/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.36/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~( 'c_lessequals'( Y,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.36/1.77 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( 'c_lessequals'(
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.36/1.77 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.36/1.77 Y, T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.36/1.77 ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 1.36/1.77 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.36/1.77 'tc_nat' ) ), 'c_Finite__Set_Ocard'( X, Y ) ) ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.36/1.77 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.36/1.77 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.36/1.77 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.36/1.77 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.36/1.77 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.36/1.77 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.36/1.77 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.36/1.77 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.36/1.77 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.36/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.36/1.77 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.36/1.77 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.36/1.77 ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.36/1.77 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.36/1.77 'c_lessequals'( T, Z, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.36/1.77 ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.36/1.77 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.36/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.36/1.77 ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.36/1.77 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.36/1.77 'c_lessequals'( Z, T, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.36/1.77 ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.36/1.77 'c_lessequals'( Y, Z, X ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.36/1.77 ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T )
% 1.36/1.77 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ]
% 1.36/1.77 ,
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.36/1.77 'c_lessequals'( Y, Z, X ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.36/1.77 ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.36/1.77 , T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ]
% 1.36/1.77 ,
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.36/1.77 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), hBOOL( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 1.36/1.77 ) ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.36/1.77 , Y ), T ), Z, X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.36/1.77 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.36/1.77 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.36/1.77 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.36/1.77 ), X ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.36/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), hBOOL( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.36/1.77 ) ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.36/1.77 ), T ), Z ), X ) ) ],
% 1.36/1.77 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.36/1.77 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.36/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.36/1.77 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.36/1.77 Y, X ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.36/1.77 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ],
% 1.36/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.36/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.36/1.78 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.36/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.36/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.36/1.78 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.36/1.78 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.36/1.78 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.36/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.36/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.36/1.78 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.36/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.36/1.78 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.36/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.36/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.36/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.36/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.36/1.78 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.36/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.36/1.78 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.36/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.36/1.78 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.36/1.78 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.36/1.78 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.78 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.36/1.78 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.78 [ =( X, Y ), ~( 'c_lessequals'( 'c_Finite__Set_Ocard'( Y, Z ),
% 1.36/1.78 'c_Finite__Set_Ocard'( X, Z ), 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.36/1.78 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.36/1.78 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.36/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_Orderings_Otop__class_Otop'( X )
% 1.36/1.78 ), 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.36/1.78 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.36/1.78 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.36/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.36/1.78 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.36/1.78 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.36/1.78 ) ), Z ) ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.36/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.36/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.36/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.36/1.78 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.36/1.78 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.36/1.78 ) ), Y ) ) ) ],
% 1.36/1.78 [ ~( =( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.36/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.36/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.78 'c_in'( X ), Y ), T ) ) ), ~( =(
% 1.36/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, 'tc_fun'( X,
% 1.36/1.78 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.36/1.78 ) ) ],
% 1.36/1.78 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.36/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.36/1.78 'c_Orderings_Otop__class_Otop'( X ), X ), Y ) ],
% 1.36/1.78 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.36/1.78 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.36/1.78 'c_Orderings_Otop__class_Otop'( X ), Y, X ), Y ) ],
% 1.36/1.78 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.36/1.78 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.36/1.78 X, 'tc_bool' ) ), Y ) ],
% 1.36/1.78 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.36/1.78 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.36/1.78 'tc_bool' ) ), X ) ],
% 1.36/1.78 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.36/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.36/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.36/1.78 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.36/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.36/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), X ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.36/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.36/1.78 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.36/1.78 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.36/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.36/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.36/1.78 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.36/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.36/1.78 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.36/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.36/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Y ) ],
% 1.36/1.78 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.36/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1'( X, Z, T ) ) ) ), ~(
% 1.36/1.78 'c_Wellfounded_Owf'( Z, T ) ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.36/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, hAPP( hAPP(
% 1.36/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.36/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ) ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.36/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.36/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.36/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ), Z ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.36/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.36/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.36/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.36/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.36/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.36/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.36/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.36/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.36/1.78 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.36/1.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.36/1.78 [ hBOOL( hAPP( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' )
% 1.36/1.78 ), Y ) ) ],
% 1.36/1.78 [ =( 'c_Finite__Set_Ocard'( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.36/1.78 ) ), 'c_Finite__Set_Ofinite'( X, Y ) ],
% 1.36/1.78 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =( hAPP(
% 1.36/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.36/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.36/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.36/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.36/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.36/1.78 [ ~( =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) )
% 1.36/1.78 , Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.36/1.78 Z ) ) ), =( Y, Z ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.36/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.36/1.78 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.36/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), hAPP( hAPP(
% 1.36/1.78 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.36/1.78 T, X ) ), 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ],
% 1.36/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.36/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.36/1.78 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.36/1.78 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.36/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.36/1.78 ],
% 1.36/1.78 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_Wellfounded_Oacyclic'(
% 1.36/1.78 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 1.36/1.78 [ 'c_Wellfounded_Oacyclic'( 'c_Relation_Oconverse'( X, Y, Y ), Y ), ~(
% 1.36/1.78 'c_Wellfounded_Oacyclic'( X, Y ) ) ],
% 1.36/1.78 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.36/1.78 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.36/1.78 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.36/1.78 , Y, 'tc_nat' ) ) ],
% 1.36/1.78 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.36/1.78 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.36/1.78 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.36/1.78 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.36/1.78 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.36/1.78 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.36/1.78 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.36/1.78 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.36/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.36/1.78 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetprod'( Y,
% 1.36/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( U,
% 1.36/1.78 'tc_bool' ) ), U, X ) ), 'c_Finite__Set_Osetprod'( Y,
% 1.36/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( U,
% 1.36/1.78 'tc_bool' ) ), U, X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.36/1.78 'c_Finite__Set_Osetprod'( Y, Z, U, X ) ), 'c_Finite__Set_Osetprod'( Y, T
% 1.36/1.78 , U, X ) ) ), ~( 'c_Finite__Set_Ofinite'( T, U ) ), ~(
% 1.36/1.78 'c_Finite__Set_Ofinite'( Z, U ) ) ],
% 1.36/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.36/1.78 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.36/1.78 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.36/1.78 X ), X ) ) ],
% 1.36/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.36/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.36/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.36/1.78 ,
% 1.36/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), ~( =(
% 1.36/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.39/1.78 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) )
% 1.39/1.78 ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ), ~( 'c_Finite__Set_Ofinite'( Y
% 1.39/1.78 , T ) ), =( 'c_Finite__Set_Osetprod'( U,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.39/1.78 'tc_bool' ) ), T, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.78 'c_Finite__Set_Osetprod'( U, Y, T, X ) ), 'c_Finite__Set_Osetprod'( U, Z
% 1.39/1.78 , T, X ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ), Y ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~(
% 1.39/1.78 'c_lessequals'( Z, Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ),
% 1.39/1.78 'c_lessequals'( Y, Z, X ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~(
% 1.39/1.78 'c_lessequals'( Y, Z, X ) ) ],
% 1.39/1.78 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), Y ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), X ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.39/1.78 , 'tc_bool' ) ), Y ) ), 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.78 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.78 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z
% 1.39/1.78 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ), X ), ~( 'c_lessequals'( U
% 1.39/1.78 , Z, X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), U ) ) ), ~( 'c_lessequals'( Y, T, X )
% 1.39/1.78 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), Z ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( T, U, 'tc_fun'( Y,
% 1.39/1.78 'tc_bool' ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ) ), hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), Z ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( T, U, 'tc_fun'( Y,
% 1.39/1.78 'tc_bool' ) ) ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ), ~(
% 1.39/1.78 'c_Finite__Set_Ofinite'( T, Y ) ) ],
% 1.39/1.78 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.39/1.78 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ],
% 1.39/1.78 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.39/1.78 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ],
% 1.39/1.78 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.39/1.78 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ],
% 1.39/1.78 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.39/1.78 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.39/1.78 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), X ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.39/1.78 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Z ), X ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.39/1.78 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.39/1.78 'c_lessequals'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.39/1.78 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.39/1.78 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.39/1.78 'c_lessequals'( Z, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.39/1.78 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.39/1.78 'c_lessequals'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.39/1.78 'c_lessequals'( Z, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 X ), Y ) ), Z ) ) ],
% 1.39/1.78 [ =( 'c_Finite__Set_Ocard'( 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.39/1.78 'c_Finite__Set_Ocard'( Y, Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ),
% 1.39/1.78 Y ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.39/1.78 'tc_bool' ) ), ~( 'c_lessequals'( X, 'c_Transitive__Closure_Ortrancl'( Z
% 1.39/1.78 , Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.39/1.78 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.39/1.78 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 1.39/1.78 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T )
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ 'c_Finite__Set_Ofinite'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ), X ), ~( 'c_Finite__Set_Ofinite'( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), X ) ),
% 1.39/1.78 ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.39/1.78 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 'tc_fun'( X, 'tc_bool' ) ), Y ), X ), ~( 'c_Finite__Set_Ofinite'(
% 1.39/1.78 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X ) ), ~(
% 1.39/1.78 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.39/1.78 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.39/1.78 ~( 'c_lessequals'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.39/1.78 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.39/1.78 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.39/1.78 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.39/1.78 ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.39/1.78 'tc_fun'( X, 'tc_bool' ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.78 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.39/1.78 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.39/1.78 'c_Set_Oinsert'( Y, Z, X ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.39/1.78 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.39/1.78 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.39/1.78 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.39/1.78 'c_lessequals'( Z, U, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ),
% 1.39/1.78 ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.39/1.78 X ) ],
% 1.39/1.78 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.39/1.78 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Set_Oinsert'( Y
% 1.39/1.78 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.39/1.78 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ],
% 1.39/1.78 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), X ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~(
% 1.39/1.78 'c_lessequals'( Y, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ),
% 1.39/1.78 'c_lessequals'( Y, Z, X ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~(
% 1.39/1.78 'c_lessequals'( Z, Y, X ) ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.39/1.78 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.39/1.78 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X
% 1.39/1.78 , 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 1.39/1.78 , 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.39/1.78 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.39/1.78 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.39/1.78 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.39/1.78 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.39/1.78 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 1.39/1.78 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, X,
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.39/1.78 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_Wellfounded_Owf'( X, Y ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ 'c_lessequals'( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.78 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z
% 1.39/1.78 ) ), 'c_Pair'( Y, T, Z, Z ) ), X ) ) ), ~( 'c_Equiv__Relations_Oequiv'(
% 1.39/1.78 U, X, Z ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), X ) ],
% 1.39/1.78 [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( Z, Y ) ), ~( 'c_lessequals'( X,
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.39/1.78 'tc_bool' ) ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.39/1.78 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.78 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.78 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.78 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.78 'c_Orderings_Otop__class_Otop'( X ) ) ), ~( =(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( X ) ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ],
% 1.39/1.78 [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.39/1.78 , 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.78 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X, Z ) ],
% 1.39/1.78 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( T, X, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.39/1.78 , X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.39/1.78 Z, X ) ), 'c_Power_Opower__class_Opower'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 'tc_nat' ) ), Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.78 , Y, X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.39/1.78 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ) ) ), =( Y, Z ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ) ) ), =( Y, Z ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.39/1.78 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.39/1.78 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.39/1.78 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Y,
% 1.39/1.78 'tc_fun'( X, 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ) ) ],
% 1.39/1.78 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), X ), 'tc_fun'(
% 1.39/1.78 Y, 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool'
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.39/1.78 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.39/1.78 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), Y )
% 1.39/1.78 ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ), Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~(
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 Y ) ) ) ],
% 1.39/1.78 [ =( 'c_Set_Ovimage'( X, hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'(
% 1.39/1.78 Y, 'tc_bool' ) ), Z ), T, Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Ovimage'( X, Z, T, Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_Set_Oinsert'( Y, T, X ), Z, 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ =( 'c_Product__Type_OSigma'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), T, Z, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 'c_Product__Type_OSigma'( X, T, Z, U ), 'c_Product__Type_OSigma'( Y, T, Z
% 1.39/1.78 , U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL( hAPP( Y, T )
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.39/1.78 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.39/1.78 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.39/1.78 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( T ), Y ), X ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( Z ), T ), X ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( T, Y, Z )
% 1.39/1.78 , 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.39/1.78 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( T ), Y ), X ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 1.39/1.78 , 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( Z ), T ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ 'c_lessequals'( 'c_Set_Ovimage'( X, Y, Z, T ), 'c_Set_Ovimage'( X, U,
% 1.39/1.78 Z, T ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, U, 'tc_fun'( T
% 1.39/1.78 , 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.39/1.78 ), Y ) ],
% 1.39/1.78 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Set_Oinsert'( Y
% 1.39/1.78 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.39/1.78 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ],
% 1.39/1.78 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.39/1.78 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.39/1.78 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.39/1.78 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.39/1.78 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.39/1.78 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.39/1.78 ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.39/1.78 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.39/1.78 ) ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.39/1.78 [ ~( =( 'c_Finite__Set_Ocard'( X, Y ), 'c_Finite__Set_Ocard'(
% 1.39/1.78 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), ~(
% 1.39/1.78 'c_Finite__Set_Ofinite'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.39/1.78 'tc_bool' ) ), Y ) ), =( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.39/1.78 'tc_bool' ) ) ) ],
% 1.39/1.78 [ =( 'c_Relation_Orel__comp'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 1.39/1.78 Z, T ), 'tc_bool' ) ), U, Z, T, W ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 1.39/1.78 , U, Z, T, W ), 'c_Relation_Orel__comp'( Y, U, Z, T, W ), 'tc_fun'(
% 1.39/1.78 'tc_prod'( Z, W ), 'tc_bool' ) ) ) ],
% 1.39/1.78 [ =( 'c_Relation_Orel__comp'( X,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 'tc_prod'(
% 1.39/1.78 T, U ), 'tc_bool' ) ), W, T, U ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 1.39/1.78 , Y, W, T, U ), 'c_Relation_Orel__comp'( X, Z, W, T, U ), 'tc_fun'(
% 1.39/1.78 'tc_prod'( W, U ), 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 1.39/1.78 , 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 1.39/1.78 , 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.39/1.78 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.78 Z, T, X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.39/1.78 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.78 T, Z, X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 1.39/1.78 'c_lessequals'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 1.39/1.78 'c_lessequals'( Z, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.39/1.78 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.78 Z, T, X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.39/1.78 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.78 T, Z, X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.39/1.78 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.39/1.78 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.39/1.78 [ 'c_Relation_Ototal__on'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ), Y, X ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 T, U, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.39/1.78 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.39/1.78 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ),
% 1.39/1.78 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.78 'tc_fun'( U, 'tc_bool' ) ), U ), T, U ) ) ) ) ],
% 1.39/1.78 [ =( 'c_Relation_Oconverse'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 1.39/1.78 Z, T ), 'tc_bool' ) ), Z, T ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Oconverse'( X,
% 1.39/1.78 Z, T ), 'c_Relation_Oconverse'( Y, Z, T ), 'tc_fun'( 'tc_prod'( T, Z ),
% 1.39/1.78 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.39/1.78 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.78 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.39/1.78 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.39/1.78 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.39/1.78 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.39/1.78 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.39/1.78 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z
% 1.39/1.78 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 1.39/1.78 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.39/1.78 , Y, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z
% 1.39/1.78 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 1.39/1.78 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.39/1.78 , Y, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.39/1.78 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Otop'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 'c_Orderings_Otop__class_Otop'( X ), X ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.39/1.78 'c_HOL_Osgn__class_Osgn'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.78 ), 'c_HOL_Oone__class_Oone'( X ) ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.39/1.78 'c_HOL_Osgn__class_Osgn'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.78 ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.39/1.78 , Z, X ), 'c_Power_Opower__class_Opower'( T, U, X ), X ), ~(
% 1.39/1.78 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.39/1.78 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.39/1.78 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.78 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.39/1.78 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.78 ), Y ) ), Z ) ), Z ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.39/1.78 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.39/1.78 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( T,
% 1.39/1.78 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z,
% 1.39/1.78 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool'
% 1.39/1.78 ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_Orderings_Obot__class_Obot'( X )
% 1.39/1.78 ), 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.39/1.78 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.39/1.78 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.39/1.78 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.39/1.78 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.39/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.39/1.78 [ =( 'c_Relation_OImage'( X,
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.39/1.78 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.78 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 1.39/1.78 'tc_fun'( U, 'tc_bool' ) ) ), ~( 'c_Relation_Osingle__valued'(
% 1.39/1.78 'c_Relation_Oconverse'( X, T, U ), U, T ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.39/1.78 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.39/1.78 T, X ) ), 'c_Power_Opower__class_Opower'( Z, T, X ) ) ), =( Z,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.39/1.78 Z, X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.39/1.78 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.39/1.78 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), Y ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.39/1.78 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ), 'c_Finite__Set_Ofinite'(
% 1.39/1.78 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ =( 'c_Relation_ORange'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 X, Y, 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ), Z, T ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_ORange'( X, Z,
% 1.39/1.78 T ), 'c_Relation_ORange'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.78 , ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.39/1.78 , Y ), T ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ],
% 1.39/1.78 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X, 'tc_fun'( Y,
% 1.39/1.78 'tc_bool' ) ), X ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), T ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.39/1.78 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.39/1.78 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.39/1.78 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 1.39/1.78 Y, X ), Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.39/1.78 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.78 T, X ), Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.39/1.78 'c_lessequals'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.39/1.78 'c_lessequals'( Y, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.39/1.78 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 1.39/1.78 Y, X ), Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.39/1.78 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.78 T, X ), Z, X ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 1.39/1.78 Y, Z, X ), X ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.39/1.78 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.39/1.78 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.39/1.78 , Z, X ), T, X ), ~( 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.39/1.78 , U, X ), T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.39/1.78 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.39/1.78 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.39/1.78 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.39/1.78 [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( T
% 1.39/1.78 , Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( Z, Y ) ) ), ~( 'c_lessequals'(
% 1.39/1.78 Z, X, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_lessequals'( X, Z, 'tc_fun'(
% 1.39/1.78 'tc_prod'( Y, Y ), 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), =( Z,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Z,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.78 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.39/1.78 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), T ) ), =( T,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), Z ) ), =( Z,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ) ],
% 1.39/1.78 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X,
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.39/1.78 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.39/1.78 X, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.39/1.78 'c_HOL_Oone__class_Oone'( X ) ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.39/1.78 'c_HOL_Oone__class_Oone'( X ) ) ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.39/1.78 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.39/1.78 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.39/1.78 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.39/1.78 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.39/1.78 T, Z, X ) ) ), =( Y, T ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.39/1.78 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) ) ), ~(
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.39/1.78 [ =( 'c_Relation_ODomain'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 X, Y, 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ), Z, T ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_ODomain'( X, Z
% 1.39/1.78 , T ), 'c_Relation_ODomain'( Y, Z, T ), 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y, hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), T ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), =( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), =( Z,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y,
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_Wellfounded_Oacc'( X, Y ), 'c_Wellfounded_Oacc'( Z
% 1.39/1.78 , Y ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'(
% 1.39/1.78 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 1.39/1.78 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.39/1.78 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.39/1.78 X, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_Finite__Set_Ocard'( X, Y ), 'c_Finite__Set_Ocard'(
% 1.39/1.78 Z, Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) )
% 1.39/1.78 , ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.39/1.78 [ =( 'c_Set_Ovimage'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y
% 1.39/1.78 , Z, 'tc_fun'( T, 'tc_bool' ) ), U, T ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Ovimage'( X, Y, U, T
% 1.39/1.78 ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Power_Opower__class_Opower'( Y
% 1.39/1.78 , Z, X ) ) ), 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.39/1.78 X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Finite__Set_Ocard'(
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1'( X, Z, T ) ) )
% 1.39/1.78 ), ~( 'c_Wellfounded_Owf'( Z, T ) ) ],
% 1.39/1.78 [ =( 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.39/1.78 'tc_bool' ) ), Y ), 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 1.39/1.78 Y, Y ), 'tc_bool' ) ), Y ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), T ) ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), T ) ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Y ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Y ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.39/1.78 [ =( 'c_Finite__Set_Ocard'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X
% 1.39/1.78 , 'tc_bool' ) ), X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.39/1.78 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Osgn__class_Osgn'( Y, X ), X ),
% 1.39/1.78 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Finite__Set_Ocard'( X, Y ) )
% 1.39/1.78 ), ~( 'c_Finite__Set_Ofinite'( X, Y ) ), =( X,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.39/1.78 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.39/1.78 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 1.39/1.78 'tc_bool' ) ), Y ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.39/1.78 'tc_bool' ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.39/1.78 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.39/1.78 [ =( 'c_Relation_ORange'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, T ), U,
% 1.39/1.78 'tc_prod'( Z, T ) ), Z, T ), 'c_Set_Oinsert'( Y, 'c_Relation_ORange'( U,
% 1.39/1.78 Z, T ), T ) ) ],
% 1.39/1.78 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.39/1.78 ), ~( 'c_lessequals'( X, hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'(
% 1.39/1.78 Z, 'tc_bool' ) ), Y ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z
% 1.39/1.78 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.39/1.78 ) ) ), 'c_lessequals'( X, hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'(
% 1.39/1.78 Z, 'tc_bool' ) ), Y ), 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.39/1.78 Y ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.39/1.78 Y ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.39/1.78 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 Y ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.39/1.78 Y ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 Y ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 Y ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.39/1.78 Y ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.39/1.78 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.39/1.78 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.39/1.78 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.39/1.78 ), Y ), T ), Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.39/1.78 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( 'c_lessequals'( Y, hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.39/1.78 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.39/1.78 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), T ), Z ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y ) ), =( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.39/1.78 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), Z ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.39/1.78 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Z ), Y ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.39/1.78 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), Z ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.39/1.78 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Z ), Y ), X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.78 X ), Y ), Z ) ), Z ), Y ) ],
% 1.39/1.78 [ ~( =( hAPP( X, 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X, Y, Z, T, U,
% 1.39/1.78 W ) ), hAPP( Y, 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X, Y, Z, T, U, W
% 1.39/1.78 ) ) ) ), =( 'c_Recdef_Ocut'( X, Z, T, U, W ), 'c_Recdef_Ocut'( Y, Z, T,
% 1.39/1.78 U, W ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.39/1.78 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 1.39/1.78 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), T
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.39/1.78 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 1.39/1.78 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), T
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.39/1.78 Y, T, X ), X ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ 'c_Relation_Osingle__valued'( 'c_Relation_OId__on'( X, Y ), Y, Y ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.39/1.78 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.39/1.78 hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ) ),
% 1.39/1.78 Y ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 X ), Y ) ), Y ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 X ), Y ) ), Y ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 X ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 X ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 X ), Y ) ), Y ) ],
% 1.39/1.78 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_Wellfounded_Oacyclic'(
% 1.39/1.78 'c_Set_Oinsert'( 'c_Pair'( Z, T, Y, Y ), X, 'tc_prod'( Y, Y ) ), Y ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'( Z, Y ) ), ~(
% 1.39/1.78 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) )
% 1.39/1.78 , ~( 'c_lessequals'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( T, 'tc_bool'
% 1.39/1.78 ) ) ), ~( hBOOL( hAPP( Z, Y ) ) ) ],
% 1.39/1.78 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_lessequals'( X, Z, 'tc_fun'(
% 1.39/1.78 'tc_prod'( Y, Y ), 'tc_bool' ) ) ), ~( 'c_Wellfounded_Oacyclic'( Z, Y ) )
% 1.39/1.78 ],
% 1.39/1.78 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_lessequals'( X, Z, 'tc_fun'( Y
% 1.39/1.78 , 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ],
% 1.39/1.78 [ 'c_Relation_Osingle__valued'( X, Y, Z ), ~(
% 1.39/1.78 'c_Relation_Osingle__valued'( T, Y, Z ) ), ~( 'c_lessequals'( X, T,
% 1.39/1.78 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.39/1.78 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.39/1.78 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.39/1.78 [ ~( =( 'c_Finite__Set_Ocard'( X, Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 'tc_nat' ) ) ), ~( 'c_Finite__Set_Ofinite'( X, Y ) ), =( X,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.78 T, U, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.39/1.78 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.39/1.78 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.39/1.78 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.39/1.78 ~( 'c_lessequals'( X, hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y,
% 1.39/1.78 'tc_bool' ) ), X ), 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_Relation_ODomain'( X, Y, Z ), 'c_Relation_ODomain'(
% 1.39/1.78 T, Y, Z ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'( X, T, 'tc_fun'(
% 1.39/1.78 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ],
% 1.39/1.78 [ =( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 1.39/1.78 , 'tc_bool' ) ), Z ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 1.39/1.78 , 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.39/1.78 Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ =( 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Y, Z, T ), U, T ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Ovimage'( X,
% 1.39/1.78 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.39/1.78 'tc_bool' ) ), T ), U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U,
% 1.39/1.78 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( X, T ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( U, T, X
% 1.39/1.78 ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( Z, Y, X
% 1.39/1.78 ), ~( 'c_lessequals'( U, T, X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.78 'c_Power_Opower__class_Opower'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.78 'c_Power_Opower__class_Opower'( Y, T, X ) ),
% 1.39/1.78 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.39/1.78 'c_Power_Opower__class_Opower'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.78 'c_Power_Opower__class_Opower'( Y, T, X ) ),
% 1.39/1.78 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z )
% 1.39/1.78 , 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ) ) ],
% 1.39/1.78 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.39/1.78 X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), W ) ) ), T
% 1.39/1.78 ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.39/1.78 X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), W
% 1.39/1.78 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Z ), W ), X ) ), ~(
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.78 ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), U ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), =( U,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.78 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z
% 1.39/1.78 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.39/1.78 'c_HOL_Osgn__class_Osgn'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.78 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.78 'c_HOL_Osgn__class_Osgn'( Y, X ) ), 'c_HOL_Osgn__class_Osgn'( Z, X ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.39/1.78 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.78 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.78 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.39/1.78 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.39/1.78 'tc_bool' ) ), Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.39/1.78 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.39/1.78 [ 'c_lessequals'( 'c_Relation_OImage'( X, Y, Z, T ), 'c_Relation_OImage'(
% 1.39/1.78 U, W, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y, W,
% 1.39/1.78 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, U, 'tc_fun'(
% 1.39/1.78 'tc_prod'( Z, T ), 'tc_bool' ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.39/1.78 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.78 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.78 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.78 ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.78 ), Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), ~( 'c_lessequals'( U
% 1.39/1.78 , Z, X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.39/1.78 'c_lessequals'( Z, Y, X ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( X, Y ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( Z ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 'tc_nat' ) ), 'c_Finite__Set_Osetprod'( X, T, Z, 'tc_nat' ) ) ) ), ~(
% 1.39/1.78 'c_Finite__Set_Ofinite'( T, Z ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.39/1.78 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 'tc_nat' ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X
% 1.39/1.78 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), Z ), 'c_Set_Oinsert'( T, U, Y ) ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Z, T ) ), hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.78 Y ), T ), U ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, 'c_Set_Oinsert'( Z, T, U ), U, X ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, Z ) ),
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, T, U, X ) ) ), hBOOL( hAPP( hAPP( 'c_in'( U
% 1.39/1.78 ), Z ), T ) ), ~( 'c_Finite__Set_Ofinite'( T, U ) ) ],
% 1.39/1.78 [ 'c_Wellfounded_Oacyclic'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, Z ), T,
% 1.39/1.78 'tc_prod'( Z, Z ) ), Z ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) )
% 1.39/1.78 , 'c_Pair'( Y, X, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( T, Z ) ) )
% 1.39/1.78 , ~( 'c_Wellfounded_Oacyclic'( T, Z ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X,
% 1.39/1.78 X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~(
% 1.39/1.78 'c_Wellfounded_Oacyclic'( 'c_Set_Oinsert'( 'c_Pair'( Z, Y, X, X ), T,
% 1.39/1.78 'tc_prod'( X, X ) ), X ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) )
% 1.39/1.78 , 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'(
% 1.39/1.78 X, T, U, Z ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 1.39/1.78 X, T, U, Z ), Z, Z ) ), U ) ), ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) )
% 1.39/1.78 , 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, T,
% 1.39/1.78 U, Z ), 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2'(
% 1.39/1.78 X, T, U, Z ), Z, Z ) ), U ) ), ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( T, Y, Z, Z ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_OImage'( Z,
% 1.39/1.78 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ), X ), X, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T
% 1.39/1.78 ) ) ), ~( 'c_Equiv__Relations_Oequiv'( T, Z, X ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), U ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Relation_OImage'( T,
% 1.39/1.78 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ), X ), X, X ), 'c_Relation_OImage'( T, 'c_Set_Oinsert'( Z,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X, X ),
% 1.39/1.78 'tc_fun'( X, 'tc_bool' ) ) ) ) ), ~( 'c_Equiv__Relations_Oequiv'( W, T, X
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), U ) ) ), ~(
% 1.39/1.78 'c_lessequals'( 'c_Relation_OImage'( T, 'c_Set_Oinsert'( Z,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X, X ),
% 1.39/1.78 'c_Relation_OImage'( T, 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X, X ),
% 1.39/1.78 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, T, X ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.78 X ), Y ), Y ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 T ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), T ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.39/1.78 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), T ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.39/1.78 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Z ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( 'c_lessequals'( Y, T, X
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( 'c_lessequals'( Z, U, X
% 1.39/1.78 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ =( 'c_Set_Ovimage'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y
% 1.39/1.78 , Z, 'tc_fun'( T, 'tc_bool' ) ), U, T ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Ovimage'( X, Y, U, T
% 1.39/1.78 ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.78 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( Y, Z )
% 1.39/1.78 ) ],
% 1.39/1.78 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.78 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( hAPP( Y, Z ), hAPP( T, Z )
% 1.39/1.78 , X ), ~( 'c_lessequals'( Y, T, 'tc_fun'( U, X ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.39/1.78 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.39/1.78 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.39/1.78 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.39/1.78 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.39/1.78 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.39/1.78 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.39/1.78 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.39/1.78 ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T, X ) ) ),
% 1.39/1.78 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T, X ) ) ),
% 1.39/1.78 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( 'c_lessequals'( T, Z,
% 1.39/1.78 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T )
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.39/1.78 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.39/1.78 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.39/1.78 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), =( Y, T ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( T, Z, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.78 X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( T, Z, 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Otop__class_Otop'(
% 1.39/1.78 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Z ) ) ),
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ), Z ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( X ), Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z,
% 1.39/1.78 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( X ), Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T,
% 1.39/1.78 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.39/1.78 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z ) ) ),
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( Z
% 1.39/1.78 ), X ), Y ) ), =( Y, T ) ],
% 1.39/1.78 [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.39/1.78 , X ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( Y, Z, X )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.39/1.78 , Z, X ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( Y, Z, X )
% 1.39/1.78 ), =( Y, Z ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.39/1.78 Y, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.39/1.78 Y, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( Y, Z, X )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( Y, Z, X )
% 1.39/1.78 ), =( Z, Y ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Z, Y ), ~( 'c_lessequals'(
% 1.39/1.78 Y, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), T ), U ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), T ), U ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( T, Z, X )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( 'c_lessequals'( Y, T, X
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, X
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( Y, T, X )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ) ), ~(
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ) ), ~(
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), 'c_lessequals'( Z, Y, X ),
% 1.39/1.78 ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.39/1.78 , Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), 'c_lessequals'( Z, Y, X ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( 'c_lessequals'( Z, Y, X
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ],
% 1.39/1.78 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), 'c_lessequals'( Z, Y, X ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), T ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.78 X ), Z ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 X ), Y ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 X ), Y ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.39/1.78 , Z ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.39/1.78 , Z ) ), Y ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.39/1.78 =( X, Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.39/1.78 [ =( X, Y ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X
% 1.39/1.78 ), Y ) ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.39/1.78 =( X, Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 'tc_nat' ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), =( X,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.39/1.78 [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.78 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.39/1.78 ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z
% 1.39/1.78 ) ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ) ), ~(
% 1.39/1.78 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ],
% 1.39/1.78 [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.78 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.39/1.78 ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z ) ), X ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( Z ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.39/1.78 , Y ), U ) ) ) ],
% 1.39/1.78 [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.78 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z
% 1.39/1.78 ) ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( Z ), Y ), U ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U
% 1.39/1.78 , X, Z ) ) ],
% 1.39/1.78 [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.78 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( Z ), Y ), U ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ),
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z ) )
% 1.39/1.78 , X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBS'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.78 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y, 'tc_bool'
% 1.39/1.78 ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T
% 1.39/1.78 , Y, X, 'tc_fun'( X, X ) ), U, Y, X, X ) ), W ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y,
% 1.39/1.78 X ), T ), 'c_Lattices_Olower__semilattice__class_Oinf'( W, Z, 'tc_fun'( Y
% 1.39/1.78 , 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), U ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( W, hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.39/1.78 Y, 'tc_bool' ) ) ) ) ), ~( 'c_Finite__Set_Ofinite'( W, Y ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.39/1.78 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.39/1.78 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.39/1.78 ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.39/1.78 ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Osgn__class_Osgn'( Y, X ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Osgn__class_Osgn'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.39/1.78 ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~(
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.39/1.78 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ),
% 1.39/1.78 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ),
% 1.39/1.78 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 X ), Y ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.78 X ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.39/1.78 X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.39/1.78 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.39/1.78 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.39/1.78 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 X ), X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.39/1.78 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.39/1.78 ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.39/1.78 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.39/1.78 Y, T, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ), =( Z, T ) ],
% 1.39/1.78 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, T ) ), 'c_Pair'(
% 1.39/1.78 U, Y, Z, T ) ), W ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, T )
% 1.39/1.78 ), 'c_Pair'( U, X, Z, T ) ), W ) ) ), ~( 'c_Relation_Osingle__valued'( W
% 1.39/1.78 , Z, T ) ) ],
% 1.39/1.78 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, T ), U ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( 'tc_prod'( W, W ) ), 'c_Pair'( Z, U, W, W ) ), V0 ) ) ),
% 1.39/1.78 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( V1, V1 ) ), 'c_Pair'( Y, T, V1,
% 1.39/1.78 V1 ) ), V2 ) ) ), ~( 'c_Equiv__Relations_Ocongruent2'( V2, V0, X, V1, W,
% 1.39/1.78 V3 ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.39/1.78 'c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1'( Z, Y, T, X ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( T, X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.39/1.78 'tc_fun'( Y, 'tc_bool' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBB'(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), Z, X, X, Y ) ), T ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.39/1.78 Y, X ), Z ), T ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Z, X ), T ), U ) ), hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Z, X ), 'c_COMBB'( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y ), T, X, X, Z ) ), U ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.39/1.78 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), X ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.39/1.78 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), X ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP(
% 1.39/1.78 'c_Nat_Osemiring__1__class_Oof__nat'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.39/1.78 hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z, 'tc_bool' ), 'tc_bool' ), X
% 1.39/1.78 ), hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z, 'tc_bool' ), 'tc_bool'
% 1.39/1.78 ), Y ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_lessequals'( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ), 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'(
% 1.39/1.78 X, 'tc_bool' ), 'tc_bool' ), Z ), 'tc_fun'( X, 'tc_bool' ) ), ~(
% 1.39/1.78 'c_lessequals'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.39/1.78 ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), T ), 'c_Relation_OImage'( U
% 1.39/1.78 , 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ), X ), X, Y ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_OImage'( Z,
% 1.39/1.78 'c_Set_Oinsert'( T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U,
% 1.39/1.78 'tc_bool' ) ), U ), U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.78 U, X ) ), 'c_Pair'( T, Y, U, X ) ), Z ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1'( Y, Z, X ) ), Y
% 1.39/1.78 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Y ) ) ), ~(
% 1.39/1.78 'c_Wellfounded_Owf'( Z, X ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1'( Y, Z, X ) ), Y ) ),
% 1.39/1.78 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Y ) ) ), ~( 'c_Wellfounded_Owf'(
% 1.39/1.78 Z, X ) ) ],
% 1.39/1.78 [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_Wellfounded_Owf'( 'c_Set_Oinsert'(
% 1.39/1.78 'c_Pair'( Z, T, Y, Y ), X, 'tc_prod'( Y, Y ) ), Y ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Relation__XImageE__1__1'( Y, Z, T, X, U ) ), Y ) ),
% 1.39/1.78 ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Relation_OImage'( T, Y, X, U )
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1'( Y, Z, T, X, U ) ), Y )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Relation_OImage'( T, Y, X
% 1.39/1.78 , U ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( 'tc_prod'(
% 1.39/1.78 X, X ), 'tc_bool' ) ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.78 X, X ) ), Y ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( 'tc_prod'(
% 1.39/1.78 X, X ), 'tc_bool' ) ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.78 X, X ) ), Y ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), ~( =( hAPP( Y,
% 1.39/1.78 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1'( Z, Y, T, X ) ),
% 1.39/1.78 'c_HOL_Oone__class_Oone'( X ) ) ), =( 'c_Finite__Set_Osetprod'( Y, Z, T,
% 1.39/1.78 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 1.39/1.78 , 'tc_bool' ) ), Z, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( Z, X ) ) ), ~( 'c_lessequals'( T, Z,
% 1.39/1.78 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), Y ), 'c_Transitive__Closure_Otrancl'( T, X )
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.78 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z
% 1.39/1.78 ) ), X ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ],
% 1.39/1.78 [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.78 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z
% 1.39/1.78 ) ), X ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, Z, T ) ) ) ),
% 1.39/1.78 ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), 'c_Wellfounded_Oacc'( Z, T ) ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.78 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, Z ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( Z, 't_a' ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, T, Z ) )
% 1.39/1.78 , 'c_Wellfounded_Oacc'( T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y
% 1.39/1.78 ), 'c_Wellfounded_Oacc'( T, Z ) ) ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1'( Y, Z, X ) ),
% 1.39/1.78 'c_Wellfounded_Oacc'( Y, X ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ),
% 1.39/1.78 'c_Wellfounded_Oacc'( Y, X ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, Z, T ) )
% 1.39/1.78 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), 'c_Wellfounded_Oacc'( Z, T
% 1.39/1.78 ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.78 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, Z ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( Z, 't_a' ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1'( Z, Y, X ) ),
% 1.39/1.78 'c_Wellfounded_Oacc'( Z, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, T, Z ) ),
% 1.39/1.78 'c_Wellfounded_Oacc'( T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y )
% 1.39/1.78 , 'c_Wellfounded_Oacc'( T, Z ) ) ) ) ],
% 1.39/1.78 [ 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 1.39/1.78 , X, Y, Y, Y ), 'c_Relation_Orel__comp'( Z, X, Y, Y, Y ), 'tc_fun'(
% 1.39/1.78 'tc_prod'( Y, Y ), 'tc_bool' ) ), Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.39/1.78 'tc_bool' ) ), Y ), ~( 'c_Wellfounded_Owf'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 1.39/1.78 Y, Y ), 'tc_bool' ) ), Y ) ) ],
% 1.39/1.78 [ 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.39/1.78 Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~(
% 1.39/1.78 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 1.39/1.78 , X, Z, Z, Z ), 'c_Relation_Orel__comp'( Y, X, Z, Z, Z ), 'tc_fun'(
% 1.39/1.78 'tc_prod'( Z, Z ), 'tc_bool' ) ), Y, 'tc_fun'( 'tc_prod'( Z, Z ),
% 1.39/1.78 'tc_bool' ) ), Z ) ) ],
% 1.39/1.78 [ =( 'c_Transitive__Closure_Otrancl'( X, Y ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_Orel__comp'(
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( X, Y ), X, Y, Y, Y ), 'tc_fun'(
% 1.39/1.78 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 1.39/1.78 [ =( 'c_Relation_ODomain'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Y,
% 1.39/1.78 Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 1.39/1.78 'tc_prod'( Y, Y ), 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ =( 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 1.39/1.78 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 1.39/1.78 [ 'c_Relation_Orefl__on'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( Y, X ), X ) ],
% 1.39/1.78 [ =( 'c_Relation_ORange'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y
% 1.39/1.78 ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_Relation_Oantisym'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Y ),
% 1.39/1.78 ~( 'c_Wellfounded_Oacyclic'( X, Y ) ) ],
% 1.39/1.78 [ 'c_Relation_Osym'( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.39/1.78 'c_Relation_Oconverse'( X, Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool'
% 1.39/1.78 ) ), Y ) ],
% 1.39/1.78 [ =( 'c_Relation_ODomain'( 'c_Relation_OId'( X ), X, X ),
% 1.39/1.78 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ =( 'c_Relation_ORange'( 'c_Relation_OId'( X ), X, X ),
% 1.39/1.78 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_Relation_Orefl__on'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.39/1.78 'tc_bool' ) ), 'c_Relation_OId'( X ), X ) ],
% 1.39/1.78 [ =( 'c_Relation_OImage'( 'c_Relation_OId__on'( X, Y ), Z, Y, Y ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( Y,
% 1.39/1.78 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 1.39/1.78 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ) ],
% 1.39/1.78 [ 'c_Relation_Oantisym'( 'c_Lattices_Oupper__semilattice__class_Osup'( X
% 1.39/1.78 , 'c_Relation_OId'( Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y )
% 1.39/1.78 , ~( 'c_Relation_Oantisym'( X, Y ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.39/1.78 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), =( Y,
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.39/1.78 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.39/1.78 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X
% 1.39/1.78 ) ), 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1'( T, Z, Y, X ) ), T
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( T,
% 1.39/1.78 Y, X ) ), 'c_Power_Opower__class_Opower'( T, Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), T
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.39/1.78 Z, X ) ), 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.39/1.78 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z )
% 1.39/1.78 , T ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( T,
% 1.39/1.78 Y, X ) ), 'c_Power_Opower__class_Opower'( T, Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), T
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.39/1.78 Z, X ) ), 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, Z, T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 Y, 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1'( Z, Y, T, X ) )
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y
% 1.39/1.78 , X ), Z ), T ) ), U ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP(
% 1.39/1.78 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'(
% 1.39/1.78 X, X ), Y ), Y, X, X ), U ) ), T ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.39/1.78 Y, X ), Z ), T ) ), U ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ),
% 1.39/1.78 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Z, X,
% 1.39/1.78 'tc_fun'( X, X ), Y ), Y, X, X ), U ) ), T ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.78 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( Y, Z ),
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, T, U, X ), X ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.78 U ), Z ), T ) ) ), ~( 'c_Finite__Set_Ofinite'( T, U ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBS'( 'c_COMBB'(
% 1.39/1.78 'c_HOL_Ominus__class_Ominus'( X ), Z, X, 'tc_fun'( X, X ), Y ), T, Y, X,
% 1.39/1.78 X ) ), U ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ), hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), T ), U ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBS'( 'c_COMBB'(
% 1.39/1.78 'c_HOL_Oplus__class_Oplus'( X ), Z, X, 'tc_fun'( X, X ), Y ), T, Y, X, X
% 1.39/1.78 ) ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ), hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), T ), U ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_in'( T ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1'( Z, Y, T, X ) ), Z
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), ~( =(
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.39/1.78 ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ), =( hAPP( Y,
% 1.39/1.78 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1'( Z, Y, T, X
% 1.39/1.78 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1'( Y, Z, T, X, U ) ), Y
% 1.39/1.78 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, U ) ), T ),
% 1.39/1.78 'c_Product__Type_OSigma'( Y, Z, X, U ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1'( Y, Z, T, X )
% 1.39/1.78 , Z, X, X ) ), T ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.78 X, X ) ), 'c_Pair'( Y, Z, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T,
% 1.39/1.78 X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1'( Y,
% 1.39/1.78 Z, T, X ), T, X, X ) ), 'c_Transitive__Closure_Ortrancl'( Y, X ) ) ), =(
% 1.39/1.78 Z, T ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, T
% 1.39/1.78 , X, X ) ), 'c_Transitive__Closure_Ortrancl'( Y, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1'( Z,
% 1.39/1.78 Y, T, X ), X, X ) ), Z ) ), =( Y, T ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.78 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 1.39/1.78 X, Z, T, U ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( U, U ) ), 'c_Pair'( Y, Z, U, U ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, U ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) )
% 1.39/1.78 , 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 1.39/1.78 X, T, U, Z ), T, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ),
% 1.39/1.78 ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z
% 1.39/1.78 ) ), 'c_Pair'( Y, T, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( U, Z )
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) )
% 1.39/1.78 , 'c_Pair'( T,
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, T,
% 1.39/1.78 U, Z ), Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( X, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ),
% 1.39/1.78 'c_Pair'( T, Y, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2'( X, Z,
% 1.39/1.78 T, U ) ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.78 'tc_prod'( U, U ) ), 'c_Pair'( Z, Y, U, U ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, U ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, Y, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Y, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~(
% 1.39/1.78 'c_Relation_Osingle__valued'( T, X, X ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( X,
% 1.39/1.78 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1'( X, Y, Z ), 't_a',
% 1.39/1.78 't_a' ) ), 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ) ) ), =( Y, X ),
% 1.39/1.78 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( X, Y
% 1.39/1.78 , 't_a', 't_a' ) ), 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ) ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, Z,
% 1.39/1.78 T, U ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.78 'tc_prod'( U, U ) ), 'c_Pair'( Z, Y, U, U ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, U ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'(
% 1.39/1.78 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1'( X, Y, Z ), Y, 't_a',
% 1.39/1.78 't_a' ) ), Z ) ), =( Y, X ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.78 't_a', 't_a' ) ), 'c_Pair'( X, Y, 't_a', 't_a' ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'(
% 1.39/1.78 X, Z, T, U ) ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( U, U ) ), 'c_Pair'( Y, Z, U, U ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, U ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1'( Y, Z, T, X )
% 1.39/1.78 , X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), =( Y, Z ), ~(
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) )
% 1.39/1.78 , 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1'( X, U, T ), T
% 1.39/1.78 , T ) ), U ) ) ), ~( 'c_Wellfounded_Owf'( U, T ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1'( X, U, T ), T, T ) ), U
% 1.39/1.78 ) ) ), ~( 'c_Wellfounded_Owf'( U, T ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.39/1.78 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1'( X, U, T ), T, T ) ), U ) )
% 1.39/1.78 ), ~( 'c_Wellfounded_Owf'( U, T ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1'( X, U, T ), T, T ) )
% 1.39/1.78 , U ) ) ), ~( 'c_Wellfounded_Owf'( U, T ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Z, X ), T, 'tc_fun'( Z, X ), 'tc_fun'( 'tc_fun'(
% 1.39/1.78 Z, 'tc_bool' ), X ), Y ), Y, 'tc_fun'( Z, 'tc_bool' ), X ), U ) ), W ),
% 1.39/1.78 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Z, X ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBC'( T, Y, Z, X ), 'tc_fun'( Y, X
% 1.39/1.78 ), 'tc_fun'( 'tc_fun'( Y, 'tc_bool' ), X ), Z ), Z, 'tc_fun'( Y,
% 1.39/1.78 'tc_bool' ), X ), W ) ), U ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X,
% 1.39/1.78 X ) ), Z ) ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1'( Z,
% 1.39/1.78 X ), 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1'(
% 1.39/1.78 Z, X ), X, X ) ), 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1'( Y, Z
% 1.39/1.78 , T, X ), T, X, X ) ), 'c_Transitive__Closure_Otrancl'( Y, X ) ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, T, X, X ) ), Y ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, T, X, X
% 1.39/1.78 ) ), 'c_Transitive__Closure_Otrancl'( Y, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1'( Z, Y, T, X ),
% 1.39/1.78 X, X ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.78 'c_Pair'( Y, T, X, X ) ), 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( X,
% 1.39/1.78 'v_sko__Transitive__Closure__Xtrancl__Xcases__1'( X, Y, Z ), 't_a', 't_a'
% 1.39/1.78 ) ), 'c_Transitive__Closure_Otrancl'( Z, 't_a' ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( X, Y, 't_a', 't_a' ) ), Z
% 1.39/1.78 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'(
% 1.39/1.78 X, Y, 't_a', 't_a' ) ), 'c_Transitive__Closure_Otrancl'( Z, 't_a' ) ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X,
% 1.39/1.78 X ) ), 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ), ~(
% 1.39/1.78 'c_Wellfounded_Oacyclic'( Z, X ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1'( Y, Z, T, X ),
% 1.39/1.78 Z, X, X ) ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.78 'c_Pair'( Y, Z, X, X ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.78 X, X ) ), 'c_Pair'( Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X
% 1.39/1.78 ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1'( Y, Z, T, X ),
% 1.39/1.78 X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ), T ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1'( Y, Z, T, X )
% 1.39/1.78 , T, X, X ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.78 'c_Pair'( Z, T, X, X ) ), 'c_Transitive__Closure_Otrancl'( Y, X ) ) ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1'( Z, Y
% 1.39/1.78 , T, X ), X, X ) ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) )
% 1.39/1.78 , 'c_Pair'( Y, T, X, X ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.78 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'(
% 1.39/1.78 'v_sko__Transitive__Closure__Xtrancl__Xcases__1'( X, Y, Z ), Y, 't_a',
% 1.39/1.78 't_a' ) ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) )
% 1.39/1.78 , 'c_Pair'( X, Y, 't_a', 't_a' ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.78 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( X, Y, 't_a', 't_a' ) ),
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( Z, 't_a' ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.78 'c_Finite__Set_Osetprod'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.78 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X,
% 1.39/1.78 X ), U, Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, U, Z, X ) ), 'c_Finite__Set_Osetprod'( T, U
% 1.39/1.78 , Z, X ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1'( Z, T, U, W, V0, Y
% 1.39/1.78 , X ), T, X, Y ) ), W ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( V0, Y
% 1.39/1.78 ) ), 'c_Pair'( Z, T, V0, Y ) ), 'c_Relation_Orel__comp'( U, W, V0, X, Y
% 1.39/1.78 ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z,
% 1.39/1.78 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1'( Z, T, U, W, X, V0
% 1.39/1.78 , Y ), X, Y ) ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, V0 )
% 1.39/1.78 ), 'c_Pair'( Z, T, X, V0 ) ), 'c_Relation_Orel__comp'( U, W, X, Y, V0 )
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ =( X, 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__XIdE__1__1'( X, Y ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Relation__XIdE__1__1'( X, Y ), Y, Y ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( 'tc_prod'( Y, Y ) ), X ), 'c_Relation_OId'( Y ) ) ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP(
% 1.39/1.78 'c_Nat_Osemiring__1__class_Oof__nat'( X ), hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBB'(
% 1.39/1.78 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z, 'tc_nat', X, Y ) ), T ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ 'c_Wellfounded_Owf'( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1'( X, Y ) ),
% 1.39/1.78 'c_Wellfounded_Oacc'( X, Y ) ) ) ) ],
% 1.39/1.78 [ 'c_Wellfounded_Owf'( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1'( X, Y ) ),
% 1.39/1.78 'c_Wellfounded_Oacc'( X, Y ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~(
% 1.39/1.78 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP(
% 1.39/1.78 'c_Nat_Osemiring__1__class_Oof__nat'( X ), 'c_Finite__Set_Osetprod'( Y, Z
% 1.39/1.78 , T, 'tc_nat' ) ), 'c_Finite__Set_Osetprod'( 'c_COMBB'(
% 1.39/1.78 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y, 'tc_nat', X, T ), Z, T, X )
% 1.39/1.78 ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.78 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, Z, X ) ), Y ) ), ~(
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Z ), 'c_Relation_OId__on'(
% 1.39/1.78 Y, X ) ) ) ) ],
% 1.39/1.78 [ =( X, 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, X,
% 1.39/1.78 Z ), 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, X, Z ), Z, Z ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), X ),
% 1.39/1.78 'c_Relation_OId__on'( Y, Z ) ) ) ) ],
% 1.39/1.78 [ =( 'c_Recdef_Ocut'( X, Y, Z, T, U ), 'c_Recdef_Ocut'( W, Y, Z, T, U )
% 1.39/1.78 ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'(
% 1.39/1.78 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X, W, Y, Z, T, U ), Z, T, T ) ),
% 1.39/1.78 Y ) ) ],
% 1.39/1.78 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 1.39/1.78 'tc_prod'( Y, Y ), 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ =( 'c_Transitive__Closure_Otrancl'(
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 1.39/1.78 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 1.39/1.78 [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 1.39/1.78 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 1.39/1.78 [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.39/1.78 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_OId'( Y ),
% 1.39/1.78 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'( X, Y ), X, Y,
% 1.39/1.78 Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 1.39/1.78 [ 'c_lessequals'( X, 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X
% 1.39/1.78 , Y, Y ), X, Y, Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~(
% 1.39/1.78 'c_Relation_Orefl__on'( Z, X, Y ) ) ],
% 1.39/1.78 [ =( 'c_Relation_ORange'( 'v_r', 't_a', 't_b' ), 'c_Relation_ODomain'(
% 1.39/1.78 'c_Relation_Oconverse'( 'v_r', 't_a', 't_b' ), 't_b', 't_a' ) ) ],
% 1.39/1.78 [ 'c_Relation_Oirrefl'( X, Y ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Y
% 1.39/1.78 , Y ) ), 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1'( X
% 1.39/1.78 , Y ), 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1'( X, Y ), Y, Y )
% 1.39/1.78 ), X ) ) ],
% 1.39/1.78 [ 'c_Equiv__Relations_Ocongruent'( X, hAPP( Y, Z ), T, U ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( W ), Z ), V0 ) ) ), ~(
% 1.39/1.78 'c_Equiv__Relations_Ocongruent2'( V1, X, Y, W, T, U ) ), ~(
% 1.39/1.78 'c_Equiv__Relations_Oequiv'( V0, V1, W ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Wellfounded_Omlex__prod'( T, U, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ), U ) ) ), ~(
% 1.39/1.78 'c_lessequals'( hAPP( T, Y ), hAPP( T, Z ), 'tc_nat' ) ) ],
% 1.39/1.78 [ 'c_Nitpick_Orefl_H'( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.78 Y, Y ) ), 'c_Pair'( 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1'( X, Y )
% 1.39/1.78 , 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1'( X, Y ), Y, Y ) ), X ) )
% 1.39/1.78 ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.39/1.78 Z, X ) ), 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.39/1.78 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_HOL_Oord__class_Oless'( 'tc_nat' ), T ), Z ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, Z, T, X ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T
% 1.39/1.78 ), 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1'( Z, Y, T, X )
% 1.39/1.78 ), Z ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X )
% 1.39/1.78 , 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.78 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.78 'tc_nat' ) ), Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), ~( =(
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.39/1.78 ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ), hBOOL( hAPP( hAPP( 'c_in'( T )
% 1.39/1.78 , 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1'( Z, Y, T,
% 1.39/1.78 X ) ), Z ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1'( Z, T, X ), X, X ) ),
% 1.39/1.78 T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), U ), Z ) ) ), ~(
% 1.39/1.78 'c_Wellfounded_Owf'( T, X ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1'( Z, T, X ), X,
% 1.39/1.78 X ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), U ), Z ) ) ), ~(
% 1.39/1.78 'c_Wellfounded_Owf'( T, X ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Relation__XImageE__1__1'( Z, T, U, X, Y ), T, X, Y )
% 1.39/1.78 ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), T ), 'c_Relation_OImage'( U
% 1.39/1.78 , Z, X, Y ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1'( Z, T, U, X, Y ), T, X
% 1.39/1.78 , Y ) ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), T ),
% 1.39/1.78 'c_Relation_OImage'( U, Z, X, Y ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.39/1.78 'c_Finite__Set_Osetprod'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.78 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z,
% 1.39/1.78 X, X ), U, Z, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ),
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, U, Z, X ) ), 'c_Finite__Set_Osetprod'( T, U
% 1.39/1.78 , Z, X ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z,
% 1.39/1.78 'c_ATP__Linkup_Osko__Relation__XDomainE__1__1'( Z, T, X, Y ), X, Y ) ), T
% 1.39/1.78 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), 'c_Relation_ODomain'( T, X
% 1.39/1.78 , Y ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z,
% 1.39/1.78 'c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1'( Z, T, X, Y ), X, Y )
% 1.39/1.78 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), 'c_Relation_ODomain'(
% 1.39/1.78 T, X, Y ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1'( Y, Z, X ), Z, X
% 1.39/1.78 , X ) ), Y ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), 'c_Wellfounded_Oacc'(
% 1.39/1.78 Y, X ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, U, T ), T
% 1.39/1.78 , T ) ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ),
% 1.39/1.78 'c_Wellfounded_Oacc'( U, T ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( Z,
% 1.39/1.78 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, T ), 't_a', 't_a' ) ), T ) ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( T,
% 1.39/1.78 't_a' ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.39/1.78 , hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1'( Z, Y, X ), Y, X,
% 1.39/1.78 X ) ), Z ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Z ),
% 1.39/1.78 'c_Wellfounded_Oacc'( T, 't_a' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.78 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( Z,
% 1.39/1.78 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, T ), 't_a', 't_a' ) ), T ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( T,
% 1.39/1.78 't_a' ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( Z,
% 1.39/1.78 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, T ), 't_a', 't_a' ) ), T ) )
% 1.39/1.78 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( T,
% 1.39/1.78 't_a' ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Z ),
% 1.39/1.78 'c_Wellfounded_Oacc'( T, 't_a' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.78 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( Z,
% 1.39/1.78 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, T ), 't_a', 't_a' ) ), T ) ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( T,
% 1.39/1.78 't_a' ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.39/1.78 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, U, T ), T, T )
% 1.39/1.78 ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), 'c_Wellfounded_Oacc'(
% 1.39/1.78 U, T ) ) ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X,
% 1.39/1.78 X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~(
% 1.39/1.78 'c_Wellfounded_Owf'( 'c_Set_Oinsert'( 'c_Pair'( Z, Y, X, X ), T,
% 1.39/1.78 'tc_prod'( X, X ) ), X ) ) ],
% 1.39/1.78 [ 'c_Wellfounded_Owf'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, Z ), T,
% 1.39/1.78 'tc_prod'( Z, Z ) ), Z ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) )
% 1.39/1.78 , 'c_Pair'( Y, X, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( T, Z ) ) )
% 1.39/1.78 , ~( 'c_Wellfounded_Owf'( T, Z ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Relation__XRangeE__1__1'( Z, T, Y, X ), Z, X, Y ) )
% 1.39/1.78 , T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), 'c_Relation_ORange'( T,
% 1.39/1.78 X, Y ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Relation__XRange__iff__1__1'( Z, T, Y, X ), Z, X, Y
% 1.39/1.78 ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), 'c_Relation_ORange'(
% 1.39/1.78 T, X, Y ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1'( Z, Y, T, X )
% 1.39/1.78 , X, X ) ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.78 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1'( Y, Z, T, X ),
% 1.39/1.78 T, X, X ) ), 'c_Transitive__Closure_Ortrancl'( Y, X ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, T, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( Y, X ) ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.78 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.78 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y, 'tc_bool' ), Z
% 1.39/1.78 ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X
% 1.39/1.78 , X ) ), Y, X, X ), U ), W, Y, X ), 'c_Power_Opower__class_Opower'( U,
% 1.39/1.78 'c_Finite__Set_Ocard'( W, Y ), X ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z )
% 1.39/1.78 , W ) ), ~( 'c_Finite__Set_Ofinite'( W, Y ) ) ],
% 1.39/1.78 [ =( 'c_Set_Ovimage'( hAPP( 'c_COMBC'( hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.78 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y, 'tc_bool'
% 1.39/1.78 ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), Y
% 1.39/1.78 , X, 'tc_fun'( X, X ) ), T ), Y, X, X ), U ), W, Y, X ), hAPP(
% 1.39/1.78 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), Z ) ), ~(
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_in'( X ), U ), W ) ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.78 X ), T ), W ) ) ],
% 1.39/1.78 [ =( 'c_Set_Ovimage'( hAPP( 'c_COMBC'( hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.78 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y, 'tc_bool'
% 1.39/1.78 ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), Y
% 1.39/1.78 , X, 'tc_fun'( X, X ) ), T ), Y, X, X ), U ), W, Y, X ),
% 1.39/1.78 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( X ), U ), W ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X )
% 1.39/1.78 , T ), W ) ) ) ],
% 1.39/1.78 [ =( 'c_Set_Ovimage'( hAPP( 'c_COMBC'( hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.78 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y, 'tc_bool'
% 1.39/1.78 ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), Y
% 1.39/1.78 , X, 'tc_fun'( X, X ) ), T ), Y, X, X ), U ), W, Y, X ),
% 1.39/1.78 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( X ), U ), W ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), T ), W ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), Z ),
% 1.39/1.78 'c_Lattices_Olower__semilattice__class_Oinf'( T, U, 'tc_fun'( Y,
% 1.39/1.78 'tc_bool' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP(
% 1.39/1.78 'c_COMBC'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'(
% 1.39/1.78 'c_in'( Y ), Y, 'tc_fun'( Y, 'tc_bool' ), 'tc_bool' ), U ), 'tc_bool',
% 1.39/1.78 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), Z, Y, X, 'tc_fun'( X, X ) ), Y, X,
% 1.39/1.78 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), T ) ), ~(
% 1.39/1.78 'c_Finite__Set_Ofinite'( T, Y ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.39/1.78 ), 'c_Relation_Oconverse'( U, Y, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.78 'tc_prod'( Y, X ) ), 'c_Pair'( T, Z, Y, X ) ), U ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.39/1.78 ), 'c_Relation_Oconverse'( U, Y, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.78 'tc_prod'( Y, X ) ), 'c_Pair'( T, Z, Y, X ) ), U ) ) ) ],
% 1.39/1.78 [ =( hAPP( 'c_Recdef_Ocut'( X, Y, Z, T, U ), W ), hAPP( X, W ) ), ~(
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( W, Z, T, T ) )
% 1.39/1.78 , Y ) ) ) ],
% 1.39/1.78 [ =( hAPP( 'c_Recdef_Ocut'( X, Y, Z, T, U ), W ), hAPP( X, W ) ), ~(
% 1.39/1.78 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( W, Z, T, T ) )
% 1.39/1.78 , Y ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.78 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.78 'c_HOL_OIf'( X ), hAPP( 'c_fequal'( Y ), Z ), 'tc_bool', 'tc_fun'( X,
% 1.39/1.78 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X ) ), Y, X, X ),
% 1.39/1.78 'c_HOL_Oone__class_Oone'( X ) ), U, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.39/1.78 ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U ) ), ~(
% 1.39/1.78 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.78 'c_HOL_OIf'( X ), hAPP( 'c_fequal'( Y ), Z ), 'tc_bool', 'tc_fun'( X,
% 1.39/1.78 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X ) ), Y, X, X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), U ), hAPP( T, Z ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( Y ), Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.78 'c_HOL_OIf'( X ), hAPP( 'c_fequal'( Y ), Z ), 'tc_bool', 'tc_fun'( X,
% 1.39/1.78 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X ) ), Y, X, X ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), U ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.78 ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U ) ), ~(
% 1.39/1.78 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.78 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.78 'c_HOL_OIf'( X ), hAPP( 'c_fequal'( Y ), Z ), 'tc_bool', 'tc_fun'( X,
% 1.39/1.78 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X ) ), Y, X, X ),
% 1.39/1.78 'c_HOL_Oone__class_Oone'( X ) ), U, Y, X ), hAPP( T, Z ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( Y ), Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Y )
% 1.39/1.78 ) ],
% 1.39/1.78 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.39/1.78 X, Y, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( T, Z ) ) ) ), hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( Z ), X ), 'c_Relation_ODomain'( T, Z, Z ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ODomain'( Z, X, X ) )
% 1.39/1.78 ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X
% 1.39/1.78 ) ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X
% 1.39/1.78 ) ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( X ), T ), 'c_Wellfounded_Oacc'( Z, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), 'c_Wellfounded_Oacc'( Z, X ) )
% 1.39/1.78 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T,
% 1.39/1.78 X, X ) ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), Y ), Z ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.78 'tc_prod'( X, X ) ), Y ), Z ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ), T ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ), T ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ), =( Y, Z ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), =( Y, Z ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), =( Y, Z ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Ortrancl'( 'c_Relation_Oconverse'( T, X, X ),
% 1.39/1.78 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z,
% 1.39/1.78 Y, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, Y, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( 'c_Relation_Oconverse'( T, X, X ), X )
% 1.39/1.78 ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Relation_Oconverse'( 'c_Transitive__Closure_Otrancl'( T, X ), X, X
% 1.39/1.78 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z
% 1.39/1.78 , X, X ) ), 'c_Transitive__Closure_Otrancl'( 'c_Relation_Oconverse'( T, X
% 1.39/1.78 , X ), X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Otrancl'( 'c_Relation_Oconverse'( T, X, X ), X
% 1.39/1.78 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z
% 1.39/1.78 , X, X ) ), 'c_Relation_Oconverse'( 'c_Transitive__Closure_Otrancl'( T, X
% 1.39/1.78 ), X, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.39/1.78 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.39/1.78 [ ~( =( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool' ),
% 1.39/1.78 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool'
% 1.39/1.78 ), 'tc_bool' ), Z ) ) ), =( Y, Z ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.39/1.78 , ~( 'c_Wellfounded_Owf'( Z, X ) ) ],
% 1.39/1.78 [ 'c_Relation_Osym'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y ), ~(
% 1.39/1.78 'c_Relation_Osym'( X, Y ) ) ],
% 1.39/1.78 [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ), 'c_Finite__Set_Ofinite'(
% 1.39/1.78 Y, X ) ],
% 1.39/1.78 [ 'c_Relation_Osym'( X, Y ), ~( 'c_Relation_Osym'(
% 1.39/1.78 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 1.39/1.78 [ 'c_Relation_Osym'( 'c_Relation_Oconverse'( X, Y, Y ), Y ), ~(
% 1.39/1.78 'c_Relation_Osym'( X, Y ) ) ],
% 1.39/1.78 [ =( 'c_Relation_ODomain'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y
% 1.39/1.78 ), 'c_Relation_ODomain'( X, Y, Y ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), ~( =( hAPP( Y,
% 1.39/1.78 Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T
% 1.39/1.78 ), Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ), =(
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, U, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.39/1.78 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), ~( =( hAPP( Y, Z ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Z
% 1.39/1.78 ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ), =(
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, U, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.39/1.78 ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.78 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ 'c_Relation_Osym'( 'c_Relation_OId'( X ), X ) ],
% 1.39/1.78 [ =( 'c_Relation_Orel__comp'( 'c_Relation_OId'( X ), Y, X, X, Z ), Y ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ =( 'c_Relation_Orel__comp'( X, 'c_Relation_OId'( Y ), Z, Y, Y ), X ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ 'c_Relation_Oantisym'( 'c_Relation_OId__on'( X, Y ), Y ) ],
% 1.39/1.78 [ 'c_Wellfounded_Owf'( 'c_Relation_Oconverse'(
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y ), Y ), ~(
% 1.39/1.78 'c_Wellfounded_Owf'( 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 1.39/1.78 [ 'c_Relation_Orefl__on'( X, Y, Z ), ~( 'c_Relation_Orefl__on'( X,
% 1.39/1.78 'c_Relation_Oconverse'( Y, Z, Z ), Z ) ) ],
% 1.39/1.78 [ 'c_Relation_Orefl__on'( X, 'c_Relation_Oconverse'( Y, Z, Z ), Z ), ~(
% 1.39/1.78 'c_Relation_Orefl__on'( X, Y, Z ) ) ],
% 1.39/1.78 [ 'c_Relation_Osym'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Y ), ~(
% 1.39/1.78 'c_Relation_Osym'( X, Y ) ) ],
% 1.39/1.78 [ 'c_Wellfounded_Owf'( 'c_Relation_Orel__comp'( X, X, Y, Y, Y ), Y ),
% 1.39/1.78 ~( 'c_Wellfounded_Owf'( X, Y ) ) ],
% 1.39/1.78 [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_Wellfounded_Owf'(
% 1.39/1.78 'c_Relation_Orel__comp'( X, X, Y, Y, Y ), Y ) ) ],
% 1.39/1.78 [ =( 'c_Relation_OImage'( 'c_Relation_OId'( X ), Y, X, X ), Y ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.39/1.78 [ =( 'c_Relation_ODomain'( 'c_Relation_OId__on'( X, Y ), Y, Y ), X ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ =( 'c_Relation_Oconverse'( X, Y, Y ), X ), ~( 'c_Relation_Osym'( X, Y
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ ~( =( 'c_Relation_Oconverse'( X, Y, Y ), X ) ), 'c_Relation_Osym'( X,
% 1.39/1.78 Y ) ],
% 1.39/1.78 [ =( 'c_Relation_ORange'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y
% 1.39/1.78 ), 'c_Relation_ORange'( X, Y, Y ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.39/1.78 'c_Finite__Set_Ofinite'( Z, T ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.78 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.39/1.78 'c_Finite__Set_Ofinite'( Z, T ) ],
% 1.39/1.78 [ =( 'c_Relation_Oconverse'( 'c_Relation_Orel__comp'( X, Y, Z, T, U ), Z
% 1.39/1.78 , U ), 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( Y, T, U ),
% 1.39/1.78 'c_Relation_Oconverse'( X, Z, T ), U, T, Z ) ) ],
% 1.39/1.78 [ 'c_Relation_Osym'( 'c_Relation_OId__on'( X, Y ), Y ) ],
% 1.39/1.78 [ 'c_Relation_Orefl__on'( X, 'c_Relation_OId__on'( X, Y ), Y ) ],
% 1.39/1.78 [ 'c_Wellfounded_Owf'( 'c_Relation_Oinv__image'( X, Y, Z, T ), T ), ~(
% 1.39/1.78 'c_Wellfounded_Owf'( X, Z ) ) ],
% 1.39/1.78 [ =( 'c_Relation_Orel__comp'( X, 'c_Transitive__Closure_Ortrancl'( X, Y
% 1.39/1.78 ), Y, Y, Y ), 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.78 X, Y ), X, Y, Y, Y ) ) ],
% 1.39/1.78 [ 'c_Relation_Osym'( 'c_Relation_Oinv__image'( X, Y, Z, T ), T ), ~(
% 1.39/1.78 'c_Relation_Osym'( X, Z ) ) ],
% 1.39/1.78 [ =( 'c_Transitive__Closure_Otrancl'( 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.78 X, Y ), Y ), 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 1.39/1.78 [ =( 'c_Relation_Oconverse'( 'c_Relation_OId'( X ), X, X ),
% 1.39/1.78 'c_Relation_OId'( X ) ) ],
% 1.39/1.78 [ 'c_Wellfounded_Owf'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y ), ~(
% 1.39/1.78 'c_Wellfounded_Owf'( X, Y ) ) ],
% 1.39/1.78 [ =( 'c_Relation_Orel__comp'( 'c_Relation_Orel__comp'( X, Y, Z, T, U ),
% 1.39/1.78 W, Z, U, V0 ), 'c_Relation_Orel__comp'( X, 'c_Relation_Orel__comp'( Y, W
% 1.39/1.78 , T, U, V0 ), Z, T, V0 ) ) ],
% 1.39/1.78 [ =( 'c_Relation_Oconverse'( 'c_Relation_Oinv__image'( X, Y, Z, T ), T,
% 1.39/1.78 T ), 'c_Relation_Oinv__image'( 'c_Relation_Oconverse'( X, Z, Z ), Y, Z, T
% 1.39/1.78 ) ) ],
% 1.39/1.78 [ =( 'c_Transitive__Closure_Otrancl'( 'c_Relation_Oconverse'( X, Y, Y )
% 1.39/1.78 , Y ), 'c_Relation_Oconverse'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y
% 1.39/1.78 , Y ) ) ],
% 1.39/1.78 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =( hAPP(
% 1.39/1.78 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), hAPP(
% 1.39/1.78 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ) ), =( Y, Z ) ],
% 1.39/1.78 [ =( 'c_Relation_Oconverse'( 'c_Relation_OId__on'( X, Y ), Y, Y ),
% 1.39/1.78 'c_Relation_OId__on'( X, Y ) ) ],
% 1.39/1.78 [ ~( =( 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X, Y, Y ), X, Y
% 1.39/1.78 , Y, Y ), X ) ), 'c_Equiv__Relations_Oequiv'( 'c_Relation_ODomain'( X, Y
% 1.39/1.78 , Y ), X, Y ) ],
% 1.39/1.78 [ 'c_Relation_Oantisym'( 'c_Relation_OId'( X ), X ) ],
% 1.39/1.78 [ 'c_Wellfounded_Owf'( 'c_Wellfounded_Omlex__prod'( X, Y, Z ), Z ), ~(
% 1.39/1.78 'c_Wellfounded_Owf'( Y, Z ) ) ],
% 1.39/1.78 [ =( 'c_Relation_ORange'( 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ),
% 1.39/1.78 'c_Relation_ODomain'( X, Y, Z ) ) ],
% 1.39/1.78 [ =( 'c_Relation_ORange'( 'c_Relation_OId__on'( X, Y ), Y, Y ), X ) ]
% 1.39/1.78 ,
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.39/1.78 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.39/1.78 [ =( 'c_Relation_Oconverse'( 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ),
% 1.39/1.78 X ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.39/1.78 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ), 'c_Finite__Set_Ofinite'( T, Y ) ],
% 1.39/1.78 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.78 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.78 ) ), 'c_Finite__Set_Ofinite'( T, Y ) ],
% 1.39/1.78 [ =( 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X, Y, Y ), X, Y, Y
% 1.39/1.78 , Y ), X ), ~( 'c_Equiv__Relations_Oequiv'( Z, X, Y ) ) ],
% 1.39/1.78 [ =( 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y, Y ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 1.39/1.78 [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'(
% 1.39/1.78 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 1.39/1.78 [ 'c_Relation_Oantisym'( 'c_Relation_Oconverse'( X, Y, Y ), Y ), ~(
% 1.39/1.78 'c_Relation_Oantisym'( X, Y ) ) ],
% 1.39/1.78 [ 'c_Relation_Orefl__on'( X, Y, Z ), ~( 'c_Equiv__Relations_Oequiv'( X,
% 1.39/1.78 Y, Z ) ) ],
% 1.39/1.78 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.78 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.78 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.39/1.78 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_Relation_Oconverse'( X, Y, Y )
% 1.39/1.78 , Y ), 'c_Relation_Oconverse'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.39/1.78 Y, Y ) ) ],
% 1.39/1.78 [ 'c_Relation_Osym'( X, Y ), ~( 'c_Equiv__Relations_Oequiv'( Z, X, Y ) )
% 1.39/1.78 ],
% 1.39/1.78 [ =( 'c_Relation_ODomain'( 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ),
% 1.39/1.78 'c_Relation_ORange'( X, Y, Z ) ) ],
% 1.39/1.78 [ =( 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_Orel__comp'(
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( X, Y ), X, Y, Y, Y ) ) ],
% 1.39/1.78 [ =( 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_Orel__comp'( X
% 1.39/1.78 , 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y, Y ) ) ],
% 1.39/1.78 [ =( 'c_Relation_ORange'( X, Y, Z ), 'c_Relation_ODomain'(
% 1.39/1.78 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ) ) ],
% 1.39/1.78 [ 'c_Relation_Ototal__on'( X, Y, Z ), ~( 'c_Relation_Ototal__on'( X,
% 1.39/1.78 'c_Relation_Oconverse'( Y, Z, Z ), Z ) ) ],
% 1.39/1.78 [ 'c_Relation_Ototal__on'( X, 'c_Relation_Oconverse'( Y, Z, Z ), Z ),
% 1.39/1.78 ~( 'c_Relation_Ototal__on'( X, Y, Z ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( X, hAPP( Y, Z ) ) ), ~( hBOOL( hAPP( 'c_Set_Ovimage'( Y,
% 1.39/1.78 X, T, U ), Z ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( 'c_Set_Ovimage'( X, Y, Z, T ), U ) ), ~( hBOOL( hAPP( Y,
% 1.39/1.78 hAPP( X, U ) ) ) ) ],
% 1.39/1.78 [ 'c_Wellfounded_Owf'( 'c_Wellfounded_Omeasure'( X, Y ), Y ) ],
% 1.39/1.78 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_Transitive__Closure_Otrancl'(
% 1.39/1.78 X, Y ), Y ), 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 1.39/1.78 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.78 X, Y ), Y ), 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.39/1.78 ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Y, X ) ), 'c_Pair'( T
% 1.39/1.78 , Z, Y, X ) ), 'c_Relation_Oconverse'( U, X, Y ) ) ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X,
% 1.39/1.78 X ) ), Z ) ) ), ~( 'c_Relation_Oirrefl'( Z, X ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ), T ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ), T ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ), T ) ) ), ~( hBOOL(
% 1.39/1.78 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ), T ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ), T ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.78 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.39/1.78 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ],
% 1.39/1.78 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.39/1.78 ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ],
% 1.39/1.78 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X,
% 1.39/1.79 X ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.79 'c_Pair'( Z, Y, X, X ) ), T ) ) ), ~( 'c_Wellfounded_Owf'( T, X ) ) ]
% 1.39/1.79 ,
% 1.39/1.79 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.39/1.79 Y, X, Z, Z ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z )
% 1.39/1.79 ), 'c_Pair'( X, Y, Z, Z ) ), T ) ) ), ~( 'c_Relation_Oantisym'( T, Z ) )
% 1.39/1.79 ],
% 1.39/1.79 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.39/1.79 Y, X, Z, Z ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z )
% 1.39/1.79 ), 'c_Pair'( X, Y, Z, Z ) ), T ) ) ), ~( 'c_Relation_Oantisym'( T, Z ) )
% 1.39/1.79 ],
% 1.39/1.79 [ =( hAPP( X, Y ), hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.79 'tc_prod'( T, T ) ), 'c_Pair'( Y, Z, T, T ) ), U ) ) ), ~(
% 1.39/1.79 'c_Equiv__Relations_Ocongruent'( U, X, T, W ) ) ],
% 1.39/1.79 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.39/1.79 X, Y, Z, Z ) ), 'c_Relation_OId__on'( T, Z ) ) ) ) ],
% 1.39/1.79 [ ~( =( 'c_Recdef_Ocut'( X, Y, Z, T, U ), 'c_Recdef_Ocut'( W, Y, Z, T, U
% 1.39/1.79 ) ) ), =( hAPP( X, V0 ), hAPP( W, V0 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.79 'tc_prod'( T, T ) ), 'c_Pair'( V0, Z, T, T ) ), Y ) ) ) ],
% 1.39/1.79 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.39/1.79 X, Y, Z, Z ) ), 'c_Relation_OId'( Z ) ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.39/1.79 ), Z ) ), ~( 'c_Nitpick_Orefl_H'( Z, X ) ) ],
% 1.39/1.79 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X,
% 1.39/1.79 X ) ), Z ) ) ), ~( 'c_Wellfounded_Owf'( Z, X ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.79 ), 'c_Relation_Oinv__image'( T, U, W, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( 'tc_prod'( W, W ) ), 'c_Pair'( hAPP( U, Y ), hAPP( U, Z ), W, W )
% 1.39/1.79 ), T ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( hAPP( Y, Z )
% 1.39/1.79 , hAPP( Y, T ), X, X ) ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.79 W, W ) ), 'c_Pair'( Z, T, W, W ) ), 'c_Relation_Oinv__image'( U, Y, X, W
% 1.39/1.79 ) ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.79 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z
% 1.39/1.79 , Y, X, X ) ), T ) ) ), ~( 'c_Relation_Osym'( T, X ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.79 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z
% 1.39/1.79 , Y, X, X ) ), T ) ) ), ~( 'c_Relation_Osym'( T, X ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.39/1.79 ), 'c_Relation_Orel__comp'( U, W, X, V0, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( 'tc_prod'( V0, Y ) ), 'c_Pair'( V1, T, V0, Y ) ), W ) ) ), ~(
% 1.39/1.79 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, V0 ) ), 'c_Pair'( Z, V1, X, V0 )
% 1.39/1.79 ), U ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.79 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ), T ) ) ), ~( hBOOL(
% 1.39/1.79 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ), T ) )
% 1.39/1.79 ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.79 ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.79 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.39/1.79 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.39/1.79 ), 'c_Relation_OId'( X ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.39/1.79 ), 'c_Relation_OId'( X ) ) ) ],
% 1.39/1.79 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.79 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.39/1.79 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.79 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ), hAPP(
% 1.39/1.79 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ) ) ) ],
% 1.39/1.79 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.39/1.79 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.79 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ), hAPP(
% 1.39/1.79 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.79 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ) ),
% 1.39/1.79 'v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1'( X, Y ) ) ), =( X, Y
% 1.39/1.79 ) ],
% 1.39/1.79 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.79 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.79 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y, 'tc_bool' ), Z
% 1.39/1.79 ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X
% 1.39/1.79 , X ) ), Y, X, X ), 'c_HOL_Oone__class_Oone'( X ) ), U, Y, X ),
% 1.39/1.79 'c_HOL_Oone__class_Oone'( X ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U )
% 1.39/1.79 ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.39/1.79 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.79 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.79 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y, 'tc_bool' ), Z
% 1.39/1.79 ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X
% 1.39/1.79 , X ) ), Y, X, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), U ), hAPP( T, Z
% 1.39/1.79 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U ) ) ), ~(
% 1.39/1.79 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.39/1.79 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.79 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.79 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y, 'tc_bool' ), Z
% 1.39/1.79 ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X
% 1.39/1.79 , X ) ), Y, X, X ), 'c_HOL_Oone__class_Oone'( X ) ), U, Y, X ), hAPP( T,
% 1.39/1.79 Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U ) ) ), ~(
% 1.39/1.79 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.39/1.79 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.79 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.79 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y, 'tc_bool' ), Z
% 1.39/1.79 ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X
% 1.39/1.79 , X ) ), Y, X, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), U ),
% 1.39/1.79 'c_HOL_Ozero__class_Ozero'( X ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U
% 1.39/1.79 ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.39/1.79 [ =( 'c_Set_Ovimage'( hAPP( 'c_COMBC'( hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.79 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y, 'tc_bool'
% 1.39/1.79 ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), Y
% 1.39/1.79 , X, 'tc_fun'( X, X ) ), T ), Y, X, X ), U ), W, Y, X ), Z ), hBOOL( hAPP(
% 1.39/1.79 hAPP( 'c_in'( X ), U ), W ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), W
% 1.39/1.79 ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.39/1.79 ), 'c_Product__Type_OSigma'( U, W, X, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( Y ), T ), hAPP( W, Z ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.79 Z ), U ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.39/1.79 ), 'c_Product__Type_OSigma'( U, W, X, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( Y ), T ), hAPP( W, Z ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.79 Z ), U ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.39/1.79 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X
% 1.39/1.79 ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ),
% 1.39/1.79 'c_Wellfounded_Oacc'( Z, X ) ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.39/1.79 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X
% 1.39/1.79 ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ),
% 1.39/1.79 'c_Wellfounded_Oacc'( Z, X ) ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_OImage'( Z, T, U, X )
% 1.39/1.79 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( U, X ) ), 'c_Pair'( W, Y,
% 1.39/1.79 U, X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), T ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_OImage'( Z, T, U, X )
% 1.39/1.79 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( U, X ) ), 'c_Pair'( W, Y,
% 1.39/1.79 U, X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), T ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ),
% 1.39/1.79 'c_Relation_OId__on'( Z, X ) ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.39/1.79 ), 'c_Relation_OId__on'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.79 Y ), Z ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( T, Y, X, X ) ), U ) ) ), ~(
% 1.39/1.79 'c_Equiv__Relations_Oequiv'( Z, U, X ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ), U ) ) ), ~(
% 1.39/1.79 'c_Equiv__Relations_Oequiv'( Z, U, X ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ORange'( Z, T, X ) )
% 1.39/1.79 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, X ) ), 'c_Pair'( U, Y, T
% 1.39/1.79 , X ) ), Z ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ORange'( Z, T, X ) )
% 1.39/1.79 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, X ) ), 'c_Pair'( U, Y, T
% 1.39/1.79 , X ) ), Z ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ODomain'( Z, X, T ) )
% 1.39/1.79 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, T ) ), 'c_Pair'( Y, U, X
% 1.39/1.79 , T ) ), Z ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ODomain'( Z, X, T ) )
% 1.39/1.79 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, T ) ), 'c_Pair'( Y, U, X
% 1.39/1.79 , T ) ), Z ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP(
% 1.39/1.79 hAPP( 'c_in'( 'tc_prod'( U, X ) ), 'c_Pair'( T, Y, U, X ) ),
% 1.39/1.79 'c_Product__Type_OSigma'( W, Z, U, X ) ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( 'tc_prod'( X, T ) ), 'c_Pair'( Y, U, X, T ) ),
% 1.39/1.79 'c_Product__Type_OSigma'( Z, W, X, T ) ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.79 ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, Y
% 1.39/1.79 , X, X ) ), T ) ), =( Z, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), U )
% 1.39/1.79 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), U ) ) ), ~(
% 1.39/1.79 'c_Relation_Ototal__on'( U, T, X ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.39/1.79 ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.39/1.79 'c_Relation_Orefl__on'( T, Z, X ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( T, Y, X, X ) ), U ) ) ), ~(
% 1.39/1.79 'c_Relation_Orefl__on'( Z, U, X ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ), U ) ) ), ~(
% 1.39/1.79 'c_Relation_Orefl__on'( Z, U, X ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.39/1.79 ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.39/1.79 'c_Relation_Orefl__on'( T, Z, X ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.79 ), 'c_Wellfounded_Omlex__prod'( T, U, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( T, Y ) ), hAPP( T, Z ) ) ) )
% 1.39/1.79 ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.79 ), 'c_Wellfounded_Omeasure'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( T, Y ) ), hAPP( T, Z ) ) ) )
% 1.39/1.79 ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( X, Y )
% 1.39/1.79 ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ),
% 1.39/1.79 'c_Pair'( Y, Z, T, T ) ), 'c_Wellfounded_Omeasure'( X, T ) ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.79 , 'c_Pair'( 'v_c____', 'v_d____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( 'v_P____' ) ) ), ~( hBOOL(
% 1.39/1.79 hAPP( hAPP( 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( 'v_c____', 'v_d____',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.79 , 'v_F'( 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), hAPP( 'c_COMBC'(
% 1.39/1.79 'c_COMBB'( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'v_h____', 'tc_nat',
% 1.39/1.79 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'v_n____' ),
% 1.39/1.79 'tc_bool', 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ),
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.79 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ), 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.79 , 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ) ), 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), hAPP( 'c_COMBC'(
% 1.39/1.79 'c_COMBB'( 'c_fequal'( 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'(
% 1.39/1.79 'tc_nat', 'tc_bool' ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'v_n____' ),
% 1.39/1.79 'tc_bool', 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ),
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'( hAPP( 'c_COMBC'(
% 1.39/1.79 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____', 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ) ), 'v_c____' ), 'tc_Arrow__Order__Mirabelle_Oindi',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ) ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.79 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ), 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.79 , 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.79 , 'c_Pair'( 'v_c____', 'v_d____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( 'c_COMBS'( 'c_COMBS'(
% 1.39/1.79 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'(
% 1.39/1.79 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.79 , 'tc_nat', 'tc_bool' ), 'v_n____' ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'(
% 1.39/1.79 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'v_e____' ),
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 1.39/1.79 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ),
% 1.39/1.79 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.79 , 'tc_nat', 'tc_bool' ), 'v_n____' ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'(
% 1.39/1.79 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____'
% 1.39/1.79 , 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ) ), 'v_c____' ), 'tc_Arrow__Order__Mirabelle_Oindi',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ) ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.79 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ), 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.79 , 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.79 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.79 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.79 hAPP( 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( 'v_c____', 'v_d____',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.79 , 'v_F'( 'v_P____' ) ) ) ) ],
% 1.39/1.79 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.39/1.79 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.39/1.79 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.39/1.79 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.79 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( hAPP(
% 1.39/1.79 'c_Arrow__Order__Mirabelle_Omktop', Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.79 , Z ) ) ), =( X, Y ), =( X, T ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.79 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( hAPP(
% 1.39/1.79 'c_Arrow__Order__Mirabelle_Omktop', Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.79 , Z ) ) ), =( Y, T ), =( X, T ) ],
% 1.39/1.79 [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) ), =( Y, W ) ]
% 1.39/1.79 ,
% 1.39/1.79 [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) ), =( X, U ) ]
% 1.39/1.79 ,
% 1.39/1.79 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.79 , 'c_Pair'( X, X, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( hAPP(
% 1.39/1.79 'c_Arrow__Order__Mirabelle_Omktop', Y ), X ) ) ) ) ],
% 1.39/1.79 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.79 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( hAPP(
% 1.39/1.79 'c_Arrow__Order__Mirabelle_Omktop', Z ), X ) ) ) ) ],
% 1.39/1.79 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ],
% 1.39/1.79 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Z, Y ), hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ],
% 1.39/1.79 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), =( Z, Y ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.39/1.79 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ), =(
% 1.39/1.79 Y, X ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.39/1.79 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), Y ) ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.39/1.79 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ), =(
% 1.39/1.79 Y, X ) ],
% 1.39/1.79 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ],
% 1.39/1.79 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), =( Z, Y ) ],
% 1.39/1.79 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.79 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ) ), Z ) ), =( Y, T ), ~( hBOOL( hAPP(
% 1.39/1.79 hAPP( 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.79 , hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omktop', Z ), T ) ) ) ) ],
% 1.39/1.79 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.39/1.79 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.39/1.79 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.79 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.39/1.79 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), X )
% 1.39/1.79 ) ) ],
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% 1.39/1.79 ],
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% 1.39/1.79 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
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% 1.39/1.79 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
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% 1.39/1.79 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
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% 1.39/1.79 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
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% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
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% 1.39/1.79 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
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% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
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% 1.39/1.79 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ) ) ],
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% 1.39/1.79 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.79 , 'c_Pair'( 'v_c____', 'v_e____', 'tc_Arrow__Order__Mirabelle_Oalt',
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% 1.39/1.79 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_HOL_Oord'( 'tc_nat' ) ],
% 1.39/1.79 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 1.39/1.79 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 1.39/1.79 [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ],
% 1.39/1.79 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 1.39/1.79 [ 'class_Lattices_Oboolean__algebra'( 'tc_bool' ) ],
% 1.39/1.79 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_bool' ) ],
% 1.39/1.79 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.39/1.79 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.39/1.79 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.39/1.79 [ 'class_Orderings_Otop'( 'tc_bool' ) ],
% 1.39/1.79 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.39/1.79 [ 'class_HOL_Oord'( 'tc_bool' ) ],
% 1.39/1.79 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.39/1.80 , W ) ) ) ],
% 1.39/1.80 [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP( hAPP( X, W ),
% 1.39/1.80 U ) ) ],
% 1.39/1.80 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.39/1.80 ,
% 1.39/1.80 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 1.39/1.80 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 1.39/1.80 ] .
% 1.39/1.80
% 1.39/1.80
% 1.39/1.80 percentage equality = 0.185398, percentage horn = 0.851029
% 1.39/1.80 This is a problem with some equality
% 1.39/1.80
% 1.39/1.80
% 1.39/1.80
% 1.39/1.80 Options Used:
% 1.39/1.80
% 1.39/1.80 useres = 1
% 1.39/1.80 useparamod = 1
% 1.39/1.80 useeqrefl = 1
% 1.39/1.80 useeqfact = 1
% 1.39/1.80 usefactor = 1
% 1.39/1.80 usesimpsplitting = 0
% 1.39/1.80 usesimpdemod = 5
% 1.39/1.80 usesimpres = 3
% 1.39/1.80
% 1.39/1.80 resimpinuse = 1000
% 1.39/1.80 resimpclauses = 20000
% 1.39/1.80 substype = eqrewr
% 1.39/1.80 backwardsubs = 1
% 1.39/1.80 selectoldest = 5
% 1.39/1.80
% 1.39/1.80 litorderings [0] = split
% 1.39/1.80 litorderings [1] = extend the termordering, first sorting on arguments
% 1.39/1.80
% 1.39/1.80 termordering = kbo
% 1.39/1.80
% 1.39/1.80 litapriori = 0
% 1.39/1.80 termapriori = 1
% 1.39/1.80 litaposteriori = 0
% 1.39/1.80 termaposteriori = 0
% 1.39/1.80 demodaposteriori = 0
% 1.39/1.80 ordereqreflfact = 0
% 1.39/1.80
% 1.39/1.80 litselect = negord
% 1.39/1.80
% 1.39/1.80 maxweight = 15
% 1.39/1.80 maxdepth = 30000
% 1.39/1.80 maxlength = 115
% 1.39/1.80 maxnrvars = 195
% 1.39/1.80 excuselevel = 1
% 1.39/1.80 increasemaxweight = 1
% 1.39/1.80
% 1.39/1.80 maxselected = 10000000
% 1.39/1.80 maxnrclauses = 10000000
% 1.39/1.80
% 1.39/1.80 showgenerated = 0
% 1.39/1.80 showkept = 0
% 1.39/1.80 showselected = 0
% 1.39/1.80 showdeleted = 0
% 1.39/1.80 showresimp = 1
% 1.39/1.80 showstatus = 2000
% 1.39/1.80
% 1.39/1.80 prologoutput = 1
% 1.39/1.80 nrgoals = 5000000
% 1.39/1.80 totalproof = 1
% 1.39/1.80
% 1.39/1.80 Symbols occurring in the translation:
% 1.39/1.80
% 1.39/1.80 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.39/1.80 . [1, 2] (w:1, o:190, a:1, s:1, b:0),
% 1.39/1.80 ! [4, 1] (w:0, o:101, a:1, s:1, b:0),
% 1.39/1.80 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.39/1.80 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Oordered__field' [40, 1] (w:1, o:110, a:1, s:
% 1.39/1.80 1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Odivision__by__zero' [41, 1] (w:1, o:115, a:1
% 1.39/1.80 , s:1, b:0),
% 1.39/1.80 'c_HOL_Ozero__class_Ozero' [42, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.39/1.80 'c_lessequals' [44, 3] (w:1, o:242, a:1, s:1, b:0),
% 1.39/1.80 'c_HOL_Oinverse__class_Odivide' [45, 1] (w:1, o:117, a:1, s:1, b:0),
% 1.39/1.80
% 1.39/1.80 hAPP [47, 2] (w:1, o:215, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Ocomm__semiring__1' [48, 1] (w:1, o:113, a:1
% 1.39/1.80 , s:1, b:0),
% 1.39/1.80 'c_HOL_Oplus__class_Oplus' [49, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.39/1.80 'class_OrderedGroup_Ocomm__monoid__add' [52, 1] (w:1, o:122, a:1, s:1
% 1.39/1.80 , b:0),
% 1.39/1.80 'tc_bool' [55, 0] (w:1, o:24, a:1, s:1, b:0),
% 1.39/1.80 'tc_fun' [56, 2] (w:1, o:216, a:1, s:1, b:0),
% 1.39/1.80 'c_Orderings_Obot__class_Obot' [57, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.39/1.80 'c_Lattices_Olower__semilattice__class_Oinf' [58, 3] (w:1, o:243, a:1
% 1.39/1.80 , s:1, b:0),
% 1.39/1.80 'class_Lattices_Obounded__lattice' [60, 1] (w:1, o:125, a:1, s:1, b:0
% 1.39/1.80 ),
% 1.39/1.80 'class_Ring__and__Field_Oordered__ring__strict' [61, 1] (w:1, o:126
% 1.39/1.80 , a:1, s:1, b:0),
% 1.39/1.80 'c_HOL_Otimes__class_Otimes' [62, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.39/1.80 'c_Transitive__Closure_Ortrancl' [64, 2] (w:1, o:217, a:1, s:1, b:0)
% 1.39/1.80 ,
% 1.39/1.80 'tc_prod' [66, 2] (w:1, o:218, a:1, s:1, b:0),
% 1.39/1.80 'c_HOL_Oone__class_Oone' [67, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.39/1.80 'c_Lattices_Oupper__semilattice__class_Osup' [68, 3] (w:1, o:244, a:1
% 1.39/1.80 , s:1, b:0),
% 1.39/1.80 'c_Relation_Osym' [69, 2] (w:1, o:219, a:1, s:1, b:0),
% 1.39/1.80 'c_Pair' [71, 4] (w:1, o:269, a:1, s:1, b:0),
% 1.39/1.80 'c_Set_Oinsert' [72, 3] (w:1, o:252, a:1, s:1, b:0),
% 1.39/1.80 'c_Relation_ODomain' [73, 3] (w:1, o:245, a:1, s:1, b:0),
% 1.39/1.80 'c_HOL_Ouminus__class_Ouminus' [74, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.39/1.80 hBOOL [75, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Opordered__ring' [76, 1] (w:1, o:135, a:1, s:
% 1.39/1.80 1, b:0),
% 1.39/1.80 'c_HOL_Ominus__class_Ominus' [77, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Oordered__semidom' [80, 1] (w:1, o:130, a:1
% 1.39/1.80 , s:1, b:0),
% 1.39/1.80 'c_Power_Opower__class_Opower' [82, 3] (w:1, o:253, a:1, s:1, b:0),
% 1.39/1.80 'tc_nat' [84, 0] (w:1, o:46, a:1, s:1, b:0),
% 1.39/1.80 'class_OrderedGroup_Olordered__ab__group__add' [85, 1] (w:1, o:137
% 1.39/1.80 , a:1, s:1, b:0),
% 1.39/1.80 'c_Relation_OImage' [87, 4] (w:1, o:270, a:1, s:1, b:0),
% 1.39/1.80 'c_Ring__and__Field_Odvd__class_Odvd' [89, 3] (w:1, o:246, a:1, s:1
% 1.39/1.80 , b:0),
% 1.39/1.80 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [90, 1]
% 1.39/1.80 (w:1, o:139, a:1, s:1, b:0),
% 1.39/1.80 'c_in' [92, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.39/1.80 'c_Set_Ovimage' [94, 4] (w:1, o:272, a:1, s:1, b:0),
% 1.39/1.80 'c_Orderings_Otop__class_Otop' [95, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.39/1.80 'class_Orderings_Obot' [96, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.39/1.80 'c_Finite__Set_Osetsum' [97, 2] (w:1, o:220, a:1, s:1, b:0),
% 1.39/1.80 'c_Finite__Set_Ofinite' [99, 2] (w:1, o:221, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Oring' [100, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.39/1.80
% 1.39/1.80 'class_OrderedGroup_Opordered__ab__group__add' [101, 1] (w:1, o:144
% 1.39/1.80 , a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Oordered__semiring__strict' [103, 1] (w:1, o:
% 1.39/1.80 131, a:1, s:1, b:0),
% 1.39/1.80 'c_HOL_Oord__class_Oless' [104, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Oidom' [106, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.39/1.80
% 1.39/1.80 'class_OrderedGroup_Oordered__ab__group__add' [108, 1] (w:1, o:138
% 1.39/1.80 , a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Oring__1' [109, 1] (w:1, o:146, a:1, s:1, b:0
% 1.39/1.80 ),
% 1.39/1.80 'class_Int_Onumber__ring' [110, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Oordered__semiring' [112, 1] (w:1, o:132, a:1
% 1.39/1.80 , s:1, b:0),
% 1.39/1.80 'class_OrderedGroup_Oab__group__add' [113, 1] (w:1, o:149, a:1, s:1
% 1.39/1.80 , b:0),
% 1.39/1.80 'class_OrderedGroup_Ogroup__add' [114, 1] (w:1, o:150, a:1, s:1, b:0)
% 1.39/1.80 ,
% 1.39/1.80 'class_Ring__and__Field_Ocomm__ring__1' [115, 1] (w:1, o:111, a:1, s:
% 1.39/1.80 1, b:0),
% 1.39/1.80 'class_OrderedGroup_Omonoid__mult' [117, 1] (w:1, o:153, a:1, s:1, b:
% 1.39/1.80 0),
% 1.39/1.80 'class_Ring__and__Field_Odvd' [118, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.39/1.80 'class_OrderedGroup_Ocomm__monoid__mult' [119, 1] (w:1, o:155, a:1
% 1.39/1.80 , s:1, b:0),
% 1.39/1.80 'c_Finite__Set_Osetprod' [120, 4] (w:1, o:274, a:1, s:1, b:0),
% 1.39/1.80 'class_OrderedGroup_Opordered__comm__monoid__add' [121, 1] (w:1, o:
% 1.39/1.80 156, a:1, s:1, b:0),
% 1.39/1.80 'c_Finite__Set_Ocard' [122, 2] (w:1, o:222, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Ofield' [123, 1] (w:1, o:157, a:1, s:1, b:0)
% 1.39/1.80 ,
% 1.39/1.80 'class_Ring__and__Field_Oring__no__zero__divisors' [124, 1] (w:1, o:
% 1.39/1.80 158, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Ono__zero__divisors' [125, 1] (w:1, o:109, a:
% 1.39/1.80 1, s:1, b:0),
% 1.39/1.80 'c_Wellfounded_Owf' [126, 2] (w:1, o:223, a:1, s:1, b:0),
% 1.39/1.80 'c_Relation_Orel__comp' [127, 5] (w:1, o:295, a:1, s:1, b:0),
% 1.39/1.80 'c_Relation_ORange' [128, 3] (w:1, o:247, a:1, s:1, b:0),
% 1.39/1.80 'c_Relation_Osingle__valued' [130, 3] (w:1, o:249, a:1, s:1, b:0),
% 1.39/1.80 'c_Relation_Orefl__on' [131, 3] (w:1, o:248, a:1, s:1, b:0),
% 1.39/1.80 'class_Lattices_Olattice' [132, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.39/1.80 'class_Lattices_Olower__semilattice' [133, 1] (w:1, o:160, a:1, s:1
% 1.39/1.80 , b:0),
% 1.39/1.80 'c_Relation_OId' [135, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.39/1.80 'class_Lattices_Oboolean__algebra' [140, 1] (w:1, o:162, a:1, s:1, b:
% 1.39/1.80 0),
% 1.39/1.80 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1' [143, 3] (w:1
% 1.39/1.80 , o:254, a:1, s:1, b:0),
% 1.39/1.80 'c_Nat_Osemiring__1__class_Oof__nat' [144, 1] (w:1, o:123, a:1, s:1
% 1.39/1.80 , b:0),
% 1.39/1.80 'class_Ring__and__Field_Osemiring__0' [145, 1] (w:1, o:164, a:1, s:1
% 1.39/1.80 , b:0),
% 1.39/1.80 'class_Power_Opower' [146, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.39/1.80 'class_Orderings_Olinorder' [147, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.39/1.80 'class_OrderedGroup_Opordered__ab__semigroup__add' [148, 1] (w:1, o:
% 1.39/1.80 166, a:1, s:1, b:0),
% 1.39/1.80 'class_Lattices_Odistrib__lattice' [149, 1] (w:1, o:178, a:1, s:1, b:
% 1.39/1.80 0),
% 1.39/1.80 'class_OrderedGroup_Olordered__ab__group__add__join' [150, 1] (w:1
% 1.39/1.80 , o:151, a:1, s:1, b:0),
% 1.39/1.80 'class_Lattices_Oupper__semilattice' [151, 1] (w:1, o:179, a:1, s:1
% 1.39/1.80 , b:0),
% 1.39/1.80 'class_Ring__and__Field_Osgn__if' [154, 1] (w:1, o:180, a:1, s:1, b:0
% 1.39/1.80 ),
% 1.39/1.80 'c_HOL_Osgn__class_Osgn' [155, 2] (w:1, o:224, a:1, s:1, b:0),
% 1.39/1.80 'class_OrderedGroup_Oab__semigroup__add' [156, 1] (w:1, o:167, a:1
% 1.39/1.80 , s:1, b:0),
% 1.39/1.80 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1' [158, 3] (w:1, o:255
% 1.39/1.80 , a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Ozero__neq__one' [159, 1] (w:1, o:181, a:1
% 1.39/1.80 , s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Omult__zero' [160, 1] (w:1, o:106, a:1, s:1
% 1.39/1.80 , b:0),
% 1.39/1.80 'c_Relation_Oconverse' [162, 3] (w:1, o:250, a:1, s:1, b:0),
% 1.39/1.80 'class_OrderedGroup_Olordered__ab__group__add__meet' [163, 1] (w:1
% 1.39/1.80 , o:152, a:1, s:1, b:0),
% 1.39/1.80 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1' [168, 3] (w:1, o:
% 1.39/1.80 256, a:1, s:1, b:0),
% 1.39/1.80 'c_Wellfounded_Oacyclic' [169, 2] (w:1, o:225, a:1, s:1, b:0),
% 1.39/1.80 'class_Orderings_Oorder' [170, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Oordered__idom' [171, 1] (w:1, o:133, a:1, s:
% 1.39/1.80 1, b:0),
% 1.39/1.80 'class_OrderedGroup_Oab__semigroup__idem__mult' [172, 1] (w:1, o:169
% 1.39/1.80 , a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Oring__1__no__zero__divisors' [173, 1] (w:1
% 1.39/1.80 , o:163, a:1, s:1, b:0),
% 1.39/1.80 'c_Equiv__Relations_Oequiv' [174, 3] (w:1, o:257, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Osemiring' [175, 1] (w:1, o:182, a:1, s:1, b:
% 1.39/1.80 0),
% 1.39/1.80 'class_Ring__and__Field_Opordered__cancel__semiring' [176, 1] (w:1
% 1.39/1.80 , o:183, a:1, s:1, b:0),
% 1.39/1.80 'c_Product__Type_OSigma' [179, 4] (w:1, o:275, a:1, s:1, b:0),
% 1.39/1.80 'class_OrderedGroup_Ocancel__ab__semigroup__add' [180, 1] (w:1, o:170
% 1.39/1.80 , a:1, s:1, b:0),
% 1.39/1.80 'class_OrderedGroup_Ocancel__semigroup__add' [181, 1] (w:1, o:171, a:
% 1.39/1.80 1, s:1, b:0),
% 1.39/1.80 'c_Relation_Ototal__on' [183, 3] (w:1, o:251, a:1, s:1, b:0),
% 1.39/1.80 'class_Orderings_Otop' [185, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Omult__mono' [186, 1] (w:1, o:107, a:1, s:1
% 1.39/1.80 , b:0),
% 1.39/1.80 'class_Ring__and__Field_Omult__mono1' [187, 1] (w:1, o:108, a:1, s:1
% 1.39/1.80 , b:0),
% 1.39/1.80 'class_Finite__Set_Ofinite_Ofinite' [188, 1] (w:1, o:184, a:1, s:1
% 1.39/1.80 , b:0),
% 1.39/1.80 'class_Orderings_Opreorder' [189, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.39/1.80 'c_Wellfounded_Oacc' [195, 2] (w:1, o:226, a:1, s:1, b:0),
% 1.39/1.80 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1' [197, 3]
% 1.39/1.80 (w:1, o:258, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Opordered__semiring' [198, 1] (w:1, o:185, a:
% 1.39/1.80 1, s:1, b:0),
% 1.39/1.80 'class_OrderedGroup_Omonoid__add' [199, 1] (w:1, o:174, a:1, s:1, b:0
% 1.39/1.80 ),
% 1.39/1.80 'c_List_Osko__Recdef__Xcuts__eq__1__1' [200, 6] (w:1, o:302, a:1, s:1
% 1.39/1.80 , b:0),
% 1.39/1.80 'c_Recdef_Ocut' [201, 5] (w:1, o:296, a:1, s:1, b:0),
% 1.39/1.80 'c_Relation_OId__on' [202, 2] (w:1, o:227, a:1, s:1, b:0),
% 1.39/1.80 'c_Relation_Oantisym' [203, 2] (w:1, o:228, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Ocomm__ring' [205, 1] (w:1, o:112, a:1, s:1
% 1.39/1.80 , b:0),
% 1.39/1.80 'class_OrderedGroup_Oab__semigroup__mult' [208, 1] (w:1, o:175, a:1
% 1.39/1.80 , s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Ocomm__semiring' [209, 1] (w:1, o:114, a:1
% 1.39/1.80 , s:1, b:0),
% 1.39/1.80 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'
% 1.39/1.80 [210, 4] (w:1, o:276, a:1, s:1, b:0),
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% 1.39/1.80 [211, 4] (w:1, o:277, a:1, s:1, b:0),
% 1.39/1.80 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1' [212, 4
% 1.39/1.80 ] (w:1, o:278, a:1, s:1, b:0),
% 1.39/1.80 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2' [213, 4
% 1.39/1.80 ] (w:1, o:279, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Oordered__comm__semiring__strict' [214, 1]
% 1.39/1.80 (w:1, o:134, a:1, s:1, b:0),
% 1.39/1.80 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [215, 1]
% 1.39/1.80 (w:1, o:176, a:1, s:1, b:0),
% 1.39/1.80 'class_HOL_Oord' [216, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.39/1.80 'c_HOL_OIf' [217, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.39/1.80 'c_COMBC' [218, 4] (w:1, o:280, a:1, s:1, b:0),
% 1.39/1.80 'c_COMBB' [219, 5] (w:1, o:297, a:1, s:1, b:0),
% 1.39/1.80 'c_COMBS' [220, 5] (w:1, o:298, a:1, s:1, b:0),
% 1.39/1.80 'c_Equiv__Relations_Ocongruent2' [227, 6] (w:1, o:303, a:1, s:1, b:0)
% 1.39/1.80 ,
% 1.39/1.80 'c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1' [228, 4] (w:1
% 1.39/1.80 , o:281, a:1, s:1, b:0),
% 1.39/1.80 'class_Ring__and__Field_Osemiring__1' [229, 1] (w:1, o:187, a:1, s:1
% 1.39/1.80 , b:0),
% 1.39/1.80 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1' [230, 3]
% 1.39/1.80 (w:1, o:259, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1' [231, 3] (w:1, o:
% 1.39/1.81 260, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Relation__XImageE__1__1' [232, 5] (w:1, o:299
% 1.39/1.81 , a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1' [233, 5] (w:1, o:
% 1.39/1.81 300, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1' [234, 4] (w:1
% 1.39/1.81 , o:282, a:1, s:1, b:0),
% 1.39/1.81 'c_Transitive__Closure_Otrancl' [235, 2] (w:1, o:229, a:1, s:1, b:0)
% 1.39/1.81 ,
% 1.39/1.81 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1' [236, 3] (w:1
% 1.39/1.81 , o:261, a:1, s:1, b:0),
% 1.39/1.81 'v_sko__Wellfounded__Xacc__Xinducts__1' [237, 2] (w:1, o:230, a:1, s:
% 1.39/1.81 1, b:0),
% 1.39/1.81 't_a' [238, 0] (w:1, o:77, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1' [239, 3]
% 1.39/1.81 (w:1, o:262, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1' [240, 3] (w:
% 1.39/1.81 1, o:263, a:1, s:1, b:0),
% 1.39/1.81 'v_sko__Wellfounded__Xacc__Xinduct__1' [241, 2] (w:1, o:231, a:1, s:1
% 1.39/1.81 , b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1' [242, 3] (w:1
% 1.39/1.81 , o:264, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1' [243, 4] (w:1
% 1.39/1.81 , o:283, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1' [244, 4
% 1.39/1.81 ] (w:1, o:284, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1' [245, 5] (w:1, o:
% 1.39/1.81 301, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1' [246, 4]
% 1.39/1.81 (w:1, o:285, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1' [247
% 1.39/1.81 , 4] (w:1, o:286, a:1, s:1, b:0),
% 1.39/1.81 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1' [250, 3] (w:1, o:
% 1.39/1.81 265, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1' [252
% 1.39/1.81 , 2] (w:1, o:232, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1' [253,
% 1.39/1.81 4] (w:1, o:287, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1' [254, 4]
% 1.39/1.81 (w:1, o:288, a:1, s:1, b:0),
% 1.39/1.81 'v_sko__Transitive__Closure__Xtrancl__Xcases__1' [255, 3] (w:1, o:266
% 1.39/1.81 , a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1' [256, 4]
% 1.39/1.81 (w:1, o:290, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1' [257, 4]
% 1.39/1.81 (w:1, o:289, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1' [258, 7] (w:1
% 1.39/1.81 , o:304, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Relation__XIdE__1__1' [259, 2] (w:1, o:233, a:1
% 1.39/1.81 , s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1' [260, 2] (w:1
% 1.39/1.81 , o:234, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1' [261, 2] (w:1, o:
% 1.39/1.81 235, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1' [262, 3] (w:1, o:267
% 1.39/1.81 , a:1, s:1, b:0),
% 1.39/1.81 'v_r' [263, 0] (w:1, o:78, a:1, s:1, b:0),
% 1.39/1.81 't_b' [264, 0] (w:1, o:79, a:1, s:1, b:0),
% 1.39/1.81 'c_Relation_Oirrefl' [265, 2] (w:1, o:236, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1' [266, 2] (w:1, o:
% 1.39/1.81 237, a:1, s:1, b:0),
% 1.39/1.81 'c_Equiv__Relations_Ocongruent' [267, 4] (w:1, o:273, a:1, s:1, b:0)
% 1.39/1.81 ,
% 1.39/1.81 'c_Wellfounded_Omlex__prod' [268, 3] (w:1, o:268, a:1, s:1, b:0),
% 1.39/1.81 'c_Nitpick_Orefl_H' [269, 2] (w:1, o:238, a:1, s:1, b:0),
% 1.39/1.81 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1' [270, 2] (w:1, o:239
% 1.39/1.81 , a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Relation__XDomainE__1__1' [271, 4] (w:1, o:291
% 1.39/1.81 , a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1' [272, 4] (w:1, o:
% 1.39/1.81 292, a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Relation__XRangeE__1__1' [274, 4] (w:1, o:293
% 1.39/1.81 , a:1, s:1, b:0),
% 1.39/1.81 'c_ATP__Linkup_Osko__Relation__XRange__iff__1__1' [275, 4] (w:1, o:
% 1.39/1.81 294, a:1, s:1, b:0),
% 1.39/1.81 'c_fequal' [276, 1] (w:1, o:188, a:1, s:1, b:0),
% 1.39/1.81 'c_Relation_Oinv__image' [277, 4] (w:1, o:271, a:1, s:1, b:0),
% 1.39/1.81 'class_Nat_Osemiring__char__0' [279, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.39/1.81
% 1.39/1.81 'c_Wellfounded_Omeasure' [280, 2] (w:1, o:240, a:1, s:1, b:0),
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' [281, 0] (w:1, o:81, a:1, s:1, b:0)
% 1.39/1.81 ,
% 1.39/1.81 'v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1' [282, 2] (w:1, o:
% 1.39/1.81 241, a:1, s:1, b:0),
% 1.39/1.81 'v_c____' [283, 0] (w:1, o:83, a:1, s:1, b:0),
% 1.39/1.81 'v_d____' [284, 0] (w:1, o:84, a:1, s:1, b:0),
% 1.39/1.81 'v_P____' [285, 0] (w:1, o:85, a:1, s:1, b:0),
% 1.39/1.81 'v_F' [286, 1] (w:1, o:189, a:1, s:1, b:0),
% 1.39/1.81 'v_h____' [287, 0] (w:1, o:86, a:1, s:1, b:0),
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oindi' [288, 0] (w:1, o:87, a:1, s:1, b:0
% 1.39/1.81 ),
% 1.39/1.81 'v_n____' [289, 0] (w:1, o:88, a:1, s:1, b:0),
% 1.39/1.81 'c_Arrow__Order__Mirabelle_Omktop' [290, 0] (w:1, o:89, a:1, s:1, b:0
% 1.39/1.81 ),
% 1.39/1.81 'v_e____' [291, 0] (w:1, o:90, a:1, s:1, b:0),
% 1.39/1.81 'c_Arrow__Order__Mirabelle_Oabove' [292, 0] (w:1, o:91, a:1, s:1, b:0
% 1.39/1.81 ),
% 1.39/1.81 'c_Arrow__Order__Mirabelle_Omkbot' [293, 0] (w:1, o:92, a:1, s:1, b:0
% 1.39/1.81 ),
% 1.39/1.81 'v_a____' [297, 0] (w:1, o:94, a:1, s:1, b:0),
% 1.39/1.81 'v_b____' [298, 0] (w:1, o:82, a:1, s:1, b:0),
% 1.39/1.81 'v_Lab____' [299, 0] (w:1, o:95, a:1, s:1, b:0),
% 1.39/1.81 'v_Lba____' [300, 0] (w:1, o:96, a:1, s:1, b:0).
% 1.39/1.81
% 1.39/1.81
% 1.39/1.81 Starting Search:
% 1.39/1.81
% 1.39/1.81
% 1.39/1.81 Bliksems!, er is een bewijs:
% 1.39/1.81 % SZS status Unsatisfiable
% 1.39/1.81 % SZS output start Refutation
% 1.39/1.81
% 1.39/1.81 clause( 1116, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.81 , 'c_Pair'( 'v_a____', 'v_b____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( hAPP( 'c_COMBC'( hAPP(
% 1.39/1.81 'c_COMBC'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'(
% 1.39/1.81 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.81 , 'tc_nat', 'tc_bool' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.39/1.81 ), 'v_n____' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), 'tc_bool',
% 1.39/1.81 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.81 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'v_Lab____' ),
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'v_Lba____' ) ) ) ) ]
% 1.39/1.81 )
% 1.39/1.81 .
% 1.39/1.81 clause( 1117, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.81 , 'c_Pair'( 'v_c____', 'v_e____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( 'c_COMBS'( 'c_COMBS'(
% 1.39/1.81 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'(
% 1.39/1.81 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.81 , 'tc_nat', 'tc_bool' ), 'v_n____' ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.81 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.81 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'(
% 1.39/1.81 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 1.39/1.81 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'v_e____' ),
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 1.39/1.81 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ),
% 1.39/1.81 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.81 , 'tc_nat', 'tc_bool' ), 'v_n____' ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.81 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.81 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'(
% 1.39/1.81 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____'
% 1.39/1.81 , 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ) ) ), 'v_c____' ), 'tc_Arrow__Order__Mirabelle_Oindi',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.81 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.81 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ) ) ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.81 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ), 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.81 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.81 , 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.81 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.81 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.81 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.82 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.82 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ) ] )
% 1.39/1.82 .
% 1.39/1.82 clause( 1118, [] )
% 1.39/1.82 .
% 1.39/1.82
% 1.39/1.82
% 1.39/1.82 % SZS output end Refutation
% 1.39/1.82 found a proof!
% 1.39/1.82
% 1.39/1.82 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.39/1.82
% 1.39/1.82 initialclauses(
% 1.39/1.82 [ clause( 1120, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1121, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1122, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1123, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1124, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 1.39/1.82 , clause( 1125, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 1.39/1.82 , clause( 1126, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 1.39/1.82 , clause( 1127, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.39/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1128, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.39/1.82 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.39/1.82 ) ) ) ] )
% 1.39/1.82 , clause( 1129, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( X ), Y, X ),
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.39/1.82 , clause( 1130, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 X ) ) ] )
% 1.39/1.82 , clause( 1131, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.39/1.82 ), X ) ] )
% 1.39/1.82 , clause( 1132, [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y )
% 1.39/1.82 , 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.39/1.82 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1133, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.39/1.82 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1134, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.39/1.82 ), X ) ) ] )
% 1.39/1.82 , clause( 1135, [ 'c_Relation_Osym'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 1.39/1.82 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Osym'( Y, Z ) ), ~(
% 1.39/1.82 'c_Relation_Osym'( X, Z ) ) ] )
% 1.39/1.82 , clause( 1136, [ =( 'c_Relation_ODomain'( 'c_Set_Oinsert'( 'c_Pair'( X, Y
% 1.39/1.82 , Z, T ), U, 'tc_prod'( Z, T ) ), Z, T ), 'c_Set_Oinsert'( X,
% 1.39/1.82 'c_Relation_ODomain'( U, Z, T ), Z ) ) ] )
% 1.39/1.82 , clause( 1137, [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.39/1.82 X, 'tc_bool' ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.39/1.82 ), 'tc_fun'( X, 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1138, [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 1.39/1.82 'c_Set_Oinsert'( Z, X, T ), Y ) ) ) ] )
% 1.39/1.82 , clause( 1139, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~(
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Z ), T ) ), W ), X ) ) ] )
% 1.39/1.82 , clause( 1140, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.39/1.82 ), W, X ) ) ] )
% 1.39/1.82 , clause( 1141, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~(
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Z ), U ) ), W ), X ) ) ] )
% 1.39/1.82 , clause( 1142, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W
% 1.39/1.82 ), X ) ) ] )
% 1.39/1.82 , clause( 1143, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1144, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1145, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z,
% 1.39/1.82 'tc_nat' ) ) ] )
% 1.39/1.82 , clause( 1146, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.39/1.82 'c_Set_Oinsert'( X, Y, Z ) ) ] )
% 1.39/1.82 , clause( 1147, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ) ] )
% 1.39/1.82 , clause( 1148, [ =( 'c_Relation_OImage'( X, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( Y, 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1149, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.39/1.82 , Z, X ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.39/1.82 'c_lessequals'( Z, T, 'tc_nat' ) ) ] )
% 1.39/1.82 , clause( 1150, [ ~(
% 1.39/1.82 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.39/1.82 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.39/1.82 Y, Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1151, [ ~(
% 1.39/1.82 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.39/1.82 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.39/1.82 Y, T, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1152, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), Z ) ) ] )
% 1.39/1.82 , clause( 1153, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 1.39/1.82 'c_Set_Oinsert'( hAPP( Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.39/1.82 T, 'tc_bool' ) ), T ), X, T ) ) ) ] )
% 1.39/1.82 , clause( 1154, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ] )
% 1.39/1.82 , clause( 1155, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.39/1.82 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1156, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.39/1.82 X, 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool'
% 1.39/1.82 ) ) ) ] )
% 1.39/1.82 , clause( 1157, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( X ), Y, X ),
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( X ) ) ] )
% 1.39/1.82 , clause( 1158, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( X ), X ), 'c_Orderings_Otop__class_Otop'(
% 1.39/1.82 X ) ) ] )
% 1.39/1.82 , clause( 1159, [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Otop__class_Otop'(
% 1.39/1.82 'tc_fun'( Y, 'tc_bool' ) ), Z, Y ), 'c_Orderings_Otop__class_Otop'(
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1160, [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ] )
% 1.39/1.82 , clause( 1161, [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.39/1.82 X, 'tc_bool' ) ), Y, 'tc_fun'( X, 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1162, [ ~( =( hAPP( hAPP( 'c_Finite__Set_Osetsum'( X, 'tc_nat' )
% 1.39/1.82 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.39/1.82 'c_Finite__Set_Ofinite'( Z, X ) ), =( hAPP( Y, T ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X
% 1.39/1.82 ), T ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1163, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), U ), Z ) ), W ) ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.39/1.82 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W ) ] )
% 1.39/1.82 , clause( 1164, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), U ), Z ) ), W ) ) ), =( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.39/1.82 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ] )
% 1.39/1.82 , clause( 1165, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ) ), U ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), T ), Z ) ), U ) ) ] )
% 1.39/1.82 , clause( 1166, [ 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 'tc_fun'( X, 'tc_bool' ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 'tc_fun'( X, 'tc_bool' ) ), Z ), 'tc_fun'( X, 'tc_bool' ) ), ~(
% 1.39/1.82 'c_lessequals'( Z, Y, 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1167, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.39/1.82 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), X ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1168, [ 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 'tc_fun'( X, 'tc_bool' ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 'tc_fun'( X, 'tc_bool' ) ), Z ), 'tc_fun'( X, 'tc_bool' ) ), ~(
% 1.39/1.82 'c_lessequals'( Z, Y, 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1169, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_lessequals'( Z, Y, X
% 1.39/1.82 ) ) ] )
% 1.39/1.82 , clause( 1170, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ] )
% 1.39/1.82 , clause( 1171, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_Finite__Set_Osetsum'( Y, X ), Z ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( T, U, 'tc_fun'( Y,
% 1.39/1.82 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( T, U, 'tc_fun'( Y,
% 1.39/1.82 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.39/1.82 hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'(
% 1.39/1.82 U, Y ) ), ~( 'c_Finite__Set_Ofinite'( T, Y ) ) ] )
% 1.39/1.82 , clause( 1172, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1173, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.82 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.82 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ),
% 1.39/1.82 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.39/1.82 , clause( 1174, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.39/1.82 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'(
% 1.39/1.82 Y, 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), T ) ) ] )
% 1.39/1.82 , clause( 1175, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Set_Oinsert'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ] )
% 1.39/1.82 , clause( 1176, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ] )
% 1.39/1.82 , clause( 1177, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1178, [ 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.39/1.82 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.39/1.82 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 1.39/1.82 Y, Y ), 'tc_bool' ) ), Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1179, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~(
% 1.39/1.82 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.39/1.82 'c_lessequals'( Z, T, X ) ) ] )
% 1.39/1.82 , clause( 1180, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.39/1.82 ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~(
% 1.39/1.82 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1181, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.39/1.82 ) ) ) ] )
% 1.39/1.82 , clause( 1182, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.39/1.82 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1183, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.39/1.82 , ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1184, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.39/1.82 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1185, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X )
% 1.39/1.82 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1186, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.39/1.82 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1187, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.39/1.82 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1188, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.39/1.82 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1189, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.39/1.82 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1190, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1191, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, X, Z ), 'tc_fun'(
% 1.39/1.82 Z, 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1192, [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.39/1.82 'c_Power_Opower__class_Opower'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.39/1.82 , Y ), Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.39/1.82 , 'c_HOL_Oone__class_Oone'( X ) ), Z, X ) ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ] )
% 1.39/1.82 , clause( 1193, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1194, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.39/1.82 'c_Finite__Set_Ofinite'( 'c_Set_Oinsert'( Z, X, Y ), Y ) ) ] )
% 1.39/1.82 , clause( 1195, [ 'c_Finite__Set_Ofinite'( 'c_Set_Oinsert'( X, Y, Z ), Z )
% 1.39/1.82 , ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ] )
% 1.39/1.82 , clause( 1196, [ 'c_Finite__Set_Ofinite'( 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( X, 'tc_bool' ) ), X ) ] )
% 1.39/1.82 , clause( 1197, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.39/1.82 'class_Int_Onumber__ring'( X ) ), ~( =( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), =( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1198, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~( hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ), T ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1199, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ), Z ) ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1200, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 Z ) ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1201, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ), T ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1202, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.39/1.82 ), T, X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1203, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z )
% 1.39/1.82 , T ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), T ), Z, X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.39/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ] )
% 1.39/1.82 , clause( 1204, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.82 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ] )
% 1.39/1.82 , clause( 1205, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.82 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ] )
% 1.39/1.82 , clause( 1206, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.39/1.82 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ] )
% 1.39/1.82 , clause( 1207, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.39/1.82 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ] )
% 1.39/1.82 , clause( 1208, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), =( Y, Z ) ] )
% 1.39/1.82 , clause( 1209, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1210, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ) ) ] )
% 1.39/1.82 , clause( 1211, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.39/1.82 , Y ) ] )
% 1.39/1.82 , clause( 1212, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ) ) ] )
% 1.39/1.82 , clause( 1213, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.39/1.82 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ) ) ] )
% 1.39/1.82 , clause( 1214, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ), X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.39/1.82 , clause( 1215, [ 'c_Finite__Set_Ofinite'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ), ~(
% 1.39/1.82 'c_Finite__Set_Ofinite'( X, Z ) ) ] )
% 1.39/1.82 , clause( 1216, [ 'c_Finite__Set_Ofinite'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ), ~(
% 1.39/1.82 'c_Finite__Set_Ofinite'( X, Z ) ) ] )
% 1.39/1.82 , clause( 1217, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'(
% 1.39/1.82 Y, Z, X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ] )
% 1.39/1.82 , clause( 1218, [ 'c_lessequals'( 'c_Relation_OImage'( X,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 1.39/1.82 'tc_fun'( U, 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1219, [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ), 'c_lessequals'( T, X,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1220, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( T, X,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1221, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.39/1.82 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Finite__Set_Osetprod'( Y, Z, T
% 1.39/1.82 , X ), 'c_Finite__Set_Osetprod'( Y, U, T, X ), X ), ~( 'c_lessequals'( Z
% 1.39/1.82 , U, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1222, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.39/1.82 X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.82 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ), Y ) ) ) ] )
% 1.39/1.82 , clause( 1223, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Y ) ) ), hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 Z ) ) ] )
% 1.39/1.82 , clause( 1224, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Y ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1225, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 T ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ] )
% 1.39/1.82 , clause( 1226, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ) ) ] )
% 1.39/1.82 , clause( 1227, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1228, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1229, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), T ) ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1230, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.82 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.39/1.82 Y ) ) ] )
% 1.39/1.82 , clause( 1231, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.39/1.82 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1232, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.39/1.82 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1233, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ) ] )
% 1.39/1.82 , clause( 1234, [ 'c_lessequals'( 'c_Finite__Set_Ocard'( X, Y ),
% 1.39/1.82 'c_Finite__Set_Ocard'( 'c_Set_Oinsert'( Z, X, Y ), Y ), 'tc_nat' ), ~(
% 1.39/1.82 'c_Finite__Set_Ofinite'( X, Y ) ) ] )
% 1.39/1.82 , clause( 1235, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ] )
% 1.39/1.82 , clause( 1236, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Z ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W
% 1.39/1.82 ) ) ) ) ] )
% 1.39/1.82 , clause( 1237, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W
% 1.39/1.82 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), T ), U ) ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ] )
% 1.39/1.82 , clause( 1238, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Z ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.39/1.82 ) ), W ) ) ) ] )
% 1.39/1.82 , clause( 1239, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U
% 1.39/1.82 ) ), W ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Z ), T ) ), W ) ) ) ) ] )
% 1.39/1.82 , clause( 1240, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) )
% 1.39/1.82 ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ), ~( 'c_Finite__Set_Ofinite'( Y
% 1.39/1.82 , T ) ), =( hAPP( hAPP( 'c_Finite__Set_Osetsum'( T, X ), U ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_Finite__Set_Osetsum'( T, X ), U ), Y ) ), hAPP( hAPP(
% 1.39/1.82 'c_Finite__Set_Osetsum'( T, X ), U ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1241, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 1.39/1.82 ) ), ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1242, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 1.39/1.82 ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1243, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 1.39/1.82 ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1244, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.39/1.82 ), Y ) ) ] )
% 1.39/1.82 , clause( 1245, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.39/1.82 T, X ) ), 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ) ] )
% 1.39/1.82 , clause( 1246, [ 'c_Wellfounded_Owf'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 1.39/1.82 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_lessequals'( 'c_Relation_Orel__comp'( X
% 1.39/1.82 , Y, Z, Z, Z ), X, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ) ), ~(
% 1.39/1.82 'c_Wellfounded_Owf'( Y, Z ) ), ~( 'c_Wellfounded_Owf'( X, Z ) ) ] )
% 1.39/1.82 , clause( 1247, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL(
% 1.39/1.82 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), Y ) ) ) ] )
% 1.39/1.82 , clause( 1248, [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ] )
% 1.39/1.82 , clause( 1249, [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ] )
% 1.39/1.82 , clause( 1250, [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Relation_ODomain'( X, Y, Y ), 'c_Relation_ORange'( Z, Y, Y ), 'tc_fun'(
% 1.39/1.82 Y, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool'
% 1.39/1.82 ) ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ), ~( 'c_Wellfounded_Owf'( X, Y
% 1.39/1.82 ) ), 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ] )
% 1.39/1.82 , clause( 1251, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ] )
% 1.39/1.82 , clause( 1252, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ] )
% 1.39/1.82 , clause( 1253, [ 'c_Relation_Osingle__valued'( 'c_Relation_Orel__comp'( X
% 1.39/1.82 , Y, Z, T, U ), Z, U ), ~( 'c_Relation_Osingle__valued'( Y, T, U ) ), ~(
% 1.39/1.82 'c_Relation_Osingle__valued'( X, Z, T ) ) ] )
% 1.39/1.82 , clause( 1254, [ 'c_Relation_Orefl__on'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( T, U,
% 1.39/1.82 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~(
% 1.39/1.82 'c_Relation_Orefl__on'( Y, U, Z ) ), ~( 'c_Relation_Orefl__on'( X, T, Z )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1255, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 1.39/1.82 , clause( 1256, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ] )
% 1.39/1.82 , clause( 1257, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ] )
% 1.39/1.82 , clause( 1258, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 1.39/1.82 , clause( 1259, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1260, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1261, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.39/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Finite__Set_Ocard'(
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ), ~(
% 1.39/1.82 'c_Finite__Set_Ofinite'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), X ) ) ] )
% 1.39/1.82 , clause( 1262, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.39/1.82 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.82 , clause( 1263, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.39/1.82 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1264, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1265, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.39/1.82 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U )
% 1.39/1.82 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), =( Z, U ), =( Y, T ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1266, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.39/1.82 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U )
% 1.39/1.82 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), =( Z, U ), =( Y, T ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1267, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.39/1.82 'c_Finite__Set_Ofinite'( 'c_Lattices_Oupper__semilattice__class_Osup'( X
% 1.39/1.82 , Z, 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ] )
% 1.39/1.82 , clause( 1268, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.39/1.82 'c_Finite__Set_Ofinite'( 'c_Lattices_Oupper__semilattice__class_Osup'( Z
% 1.39/1.82 , X, 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ] )
% 1.39/1.82 , clause( 1269, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ] )
% 1.39/1.82 , clause( 1270, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( X ), Y, X ), Y ) ] )
% 1.39/1.82 , clause( 1271, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.39/1.82 X, 'tc_bool' ) ), Y ) ] )
% 1.39/1.82 , clause( 1272, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.39/1.82 'tc_bool' ) ), X ) ] )
% 1.39/1.82 , clause( 1273, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.39/1.82 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1274, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.39/1.82 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ) ) ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.39/1.82 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.82 , clause( 1275, [ 'c_Relation_Orefl__on'( 'c_Orderings_Otop__class_Otop'(
% 1.39/1.82 'tc_fun'( X, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 Y, 'c_Relation_OId'( X ), 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' ) ), X )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1276, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1277, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( X ) ) ), =( Z,
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( X ) ) ] )
% 1.39/1.82 , clause( 1278, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( X ) ) ), =( Y,
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( X ) ) ] )
% 1.39/1.82 , clause( 1279, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.82 , X ) ] )
% 1.39/1.82 , clause( 1280, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1281, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.82 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1282, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.39/1.82 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1283, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ] )
% 1.39/1.82 , clause( 1284, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ] )
% 1.39/1.82 , clause( 1285, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ] )
% 1.39/1.82 , clause( 1286, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1287, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1288, [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.39/1.82 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Relation_OImage'( Z, X, Y, Y )
% 1.39/1.82 , 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ) ] )
% 1.39/1.82 , clause( 1289, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1290, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1291, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Y,
% 1.39/1.82 'tc_fun'( X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1292, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), X ), 'tc_fun'(
% 1.39/1.82 Y, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool'
% 1.39/1.82 ) ) ) ] )
% 1.39/1.82 , clause( 1293, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.39/1.82 , clause( 1294, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.39/1.82 , clause( 1295, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.82 'c_HOL_Oone__class_Oone'( X ) ), Y ), Y ) ] )
% 1.39/1.82 , clause( 1296, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'(
% 1.39/1.82 X ) ), Y ), Y ) ] )
% 1.39/1.82 , clause( 1297, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.39/1.82 , Y ), Y ) ] )
% 1.39/1.82 , clause( 1298, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X
% 1.39/1.82 ) ), Y ) ] )
% 1.39/1.82 , clause( 1299, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.39/1.82 'c_HOL_Oone__class_Oone'( X ) ), Y ) ] )
% 1.39/1.82 , clause( 1300, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.82 'c_HOL_Oone__class_Oone'( X ) ), Y ), Y ) ] )
% 1.39/1.82 , clause( 1301, [ ~(
% 1.39/1.82 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.39/1.82 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( 'c_lessequals'( Y, T, X
% 1.39/1.82 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1302, [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ] )
% 1.39/1.82 , clause( 1303, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ] )
% 1.39/1.82 , clause( 1304, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ] )
% 1.39/1.82 , clause( 1305, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.82 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1'( X, Z, T ) ) ) ),
% 1.39/1.82 ~( 'c_Wellfounded_Owf'( Z, T ) ) ] )
% 1.39/1.82 , clause( 1306, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), U ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), U ) )
% 1.39/1.82 ), ~( 'c_lessequals'( Y, T, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1307, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( Y, Z, X ) ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.39/1.82 ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1308, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.39/1.82 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), hAPP(
% 1.39/1.82 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1309, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ),
% 1.39/1.82 hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ), X ), ~(
% 1.39/1.82 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 1.39/1.82 , clause( 1310, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1311, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.39/1.82 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.39/1.82 X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 1.39/1.82 , clause( 1312, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.39/1.82 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.39/1.82 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1313, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.39/1.82 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.39/1.82 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1314, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 1.39/1.82 T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1315, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_Set_Oinsert'( T, X, Z ), Y, 'tc_fun'( Z, 'tc_bool' ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1316, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 1.39/1.82 , clause( 1317, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1318, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1319, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.39/1.82 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1320, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.39/1.82 X ), Y ), Z ) ), Z ), Y ) ] )
% 1.39/1.82 , clause( 1321, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ),
% 1.39/1.82 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), Z ) ) ) ) ] )
% 1.39/1.82 , clause( 1322, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 1.39/1.82 ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.39/1.82 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.39/1.82 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1323, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1324, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 1.39/1.82 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1325, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ] )
% 1.39/1.82 , clause( 1326, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 1.39/1.82 , clause( 1327, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ] )
% 1.39/1.82 , clause( 1328, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1329, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.39/1.82 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1330, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ] )
% 1.39/1.82 , clause( 1331, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'(
% 1.39/1.82 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ] )
% 1.39/1.82 , clause( 1332, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'(
% 1.39/1.82 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 1.39/1.82 , clause( 1333, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ] )
% 1.39/1.82 , clause( 1334, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 1.39/1.82 , clause( 1335, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.39/1.82 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1336, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X,
% 1.39/1.82 'tc_fun'( Y, 'tc_bool' ) ), X ) ] )
% 1.39/1.82 , clause( 1337, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ] )
% 1.39/1.82 , clause( 1338, [ 'c_lessequals'( 'c_Relation_Orel__comp'( X, Y, Z, T, U )
% 1.39/1.82 , 'c_Relation_Orel__comp'( W, V0, Z, T, U ), 'tc_fun'( 'tc_prod'( Z, U )
% 1.39/1.82 , 'tc_bool' ) ), ~( 'c_lessequals'( Y, V0, 'tc_fun'( 'tc_prod'( T, U ),
% 1.39/1.82 'tc_bool' ) ) ), ~( 'c_lessequals'( X, W, 'tc_fun'( 'tc_prod'( Z, T ),
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1339, [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.39/1.82 'c_HOL_Osgn__class_Osgn'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.82 ), 'c_HOL_Oone__class_Oone'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.82 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1340, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.82 X ), Y ), Z ) ), T ) ) ] )
% 1.39/1.82 , clause( 1341, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 1.39/1.82 , clause( 1342, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.39/1.82 , clause( 1343, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 1.39/1.82 , clause( 1344, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.39/1.82 , clause( 1345, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.82 X ), Y ), Z ) ), T ) ) ] )
% 1.39/1.82 , clause( 1346, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.82 X ), Y ), T ) ), Z ) ) ] )
% 1.39/1.82 , clause( 1347, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 1.39/1.82 , clause( 1348, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 1.39/1.82 , clause( 1349, [ =( 'c_Relation_OImage'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 1.39/1.82 Z, T ), 'tc_bool' ) ), U, Z, T ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_OImage'( X, U,
% 1.39/1.82 Z, T ), 'c_Relation_OImage'( Y, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1350, [ =( 'c_Relation_OImage'( X,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), T, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 1.39/1.82 'tc_fun'( U, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1351, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.82 ), Y ) ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ] )
% 1.39/1.82 , clause( 1352, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.82 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1'( X, Z, T ) ) ) ), ~(
% 1.39/1.82 'c_Wellfounded_Owf'( Z, T ) ) ] )
% 1.39/1.82 , clause( 1353, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.39/1.82 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 1.39/1.82 , clause( 1354, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ] )
% 1.39/1.82 , clause( 1355, [ 'c_lessequals'( 'c_Relation_OImage'( X, Y, Z, T ), U,
% 1.39/1.82 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Relation_OImage'( 'c_Relation_Oconverse'( X, Z, T ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( T, 'tc_bool' ) ), U ), T, Z ) )
% 1.39/1.82 , 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1356, [ 'c_lessequals'( X, hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 'tc_fun'( Y, 'tc_bool' ) ), 'c_Relation_OImage'( 'c_Relation_Oconverse'(
% 1.39/1.82 Z, Y, T ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( T, 'tc_bool' )
% 1.39/1.82 ), U ), T, Y ) ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_Relation_OImage'( Z, X, Y, T ), U, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1357, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 1.39/1.82 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ] )
% 1.39/1.82 , clause( 1358, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.39/1.82 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.39/1.82 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 1.39/1.82 , clause( 1359, [ 'c_Relation_Osingle__valued'( 'c_Relation_OId'( X ), X, X
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1360, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ] )
% 1.39/1.82 , clause( 1361, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1362, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'(
% 1.39/1.82 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ] )
% 1.39/1.82 , clause( 1363, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'(
% 1.39/1.82 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 1.39/1.82 , clause( 1364, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ] )
% 1.39/1.82 , clause( 1365, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 1.39/1.82 , clause( 1366, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ] )
% 1.39/1.82 , clause( 1367, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1368, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ] )
% 1.39/1.82 , clause( 1369, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1370, [ ~(
% 1.39/1.82 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 1.39/1.82 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1371, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T,
% 1.39/1.82 'tc_nat' ) ) ] )
% 1.39/1.82 , clause( 1372, [ 'c_Finite__Set_Ofinite'( X, Y ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 'tc_nat' ) ), 'c_Finite__Set_Ocard'( X, Y ) ) ) ) ] )
% 1.39/1.82 , clause( 1373, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1374, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.39/1.82 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ] )
% 1.39/1.82 , clause( 1375, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ] )
% 1.39/1.82 , clause( 1376, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ] )
% 1.39/1.82 , clause( 1377, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1378, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1379, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.39/1.82 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.39/1.82 'c_lessequals'( T, Z, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1380, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1381, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.39/1.82 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.39/1.82 'c_lessequals'( Z, T, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1382, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.82 ) ), 'c_lessequals'( Y, Z, X ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.82 ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T )
% 1.39/1.82 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1383, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.82 ) ), 'c_lessequals'( Y, Z, X ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.82 ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.39/1.82 , T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1384, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.39/1.82 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.39/1.82 , Y ), T ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1385, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.39/1.82 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.39/1.82 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.39/1.82 ), X ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ] )
% 1.39/1.82 , clause( 1386, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.39/1.82 ), T ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1387, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.39/1.82 Y, X ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ] )
% 1.39/1.82 , clause( 1388, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1389, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1390, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ] )
% 1.39/1.82 , clause( 1391, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 1.39/1.82 ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1392, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 1.39/1.82 ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1393, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1394, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.82 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1395, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1396, [ =( X, Y ), ~( 'c_lessequals'( 'c_Finite__Set_Ocard'( Y, Z
% 1.39/1.82 ), 'c_Finite__Set_Ocard'( X, Z ), 'tc_nat' ) ), ~( 'c_lessequals'( X, Y
% 1.39/1.82 , 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ] )
% 1.39/1.82 , clause( 1397, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_Orderings_Otop__class_Otop'( X )
% 1.39/1.82 ), 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.39/1.82 , clause( 1398, [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) )
% 1.39/1.82 ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1399, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.82 X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ), Z ) ) ] )
% 1.39/1.82 , clause( 1400, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.82 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ] )
% 1.39/1.82 , clause( 1401, [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.39/1.82 X, 'tc_bool' ) ), Y ) ) ) ] )
% 1.39/1.82 , clause( 1402, [ ~( =( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.39/1.82 ) ) ] )
% 1.39/1.82 , clause( 1403, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.39/1.82 ) ) ] )
% 1.39/1.82 , clause( 1404, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( X ), X ), Y ) ] )
% 1.39/1.82 , clause( 1405, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( X ), Y, X ), Y ) ] )
% 1.39/1.82 , clause( 1406, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.39/1.82 X, 'tc_bool' ) ), Y ) ] )
% 1.39/1.82 , clause( 1407, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.39/1.82 'tc_bool' ) ), X ) ] )
% 1.39/1.82 , clause( 1408, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), X ) ] )
% 1.39/1.82 , clause( 1409, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.39/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1410, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.39/1.82 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1411, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Y ) ] )
% 1.39/1.82 , clause( 1412, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.82 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1'( X, Z, T ) ) ) ), ~(
% 1.39/1.82 'c_Wellfounded_Owf'( Z, T ) ) ] )
% 1.39/1.82 , clause( 1413, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ) ) ] )
% 1.39/1.82 , clause( 1414, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ), Z ) ] )
% 1.39/1.82 , clause( 1415, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1416, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1417, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.39/1.82 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1418, [ hBOOL( hAPP( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X
% 1.39/1.82 , 'tc_bool' ) ), Y ) ) ] )
% 1.39/1.82 , clause( 1419, [ =( 'c_Finite__Set_Ocard'( X, Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Finite__Set_Ofinite'( X, Y )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1420, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ] )
% 1.39/1.82 , clause( 1421, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ] )
% 1.39/1.82 , clause( 1422, [ ~( =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), Z ) ) ), =( Y, Z ) ] )
% 1.39/1.82 , clause( 1423, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.39/1.82 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.39/1.82 T, X ) ), 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ] )
% 1.39/1.82 , clause( 1424, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Oone__class_Oone'( X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.39/1.82 ) ) ) ] )
% 1.39/1.82 , clause( 1425, [ 'c_Wellfounded_Oacyclic'( X, Y ), ~(
% 1.39/1.82 'c_Wellfounded_Oacyclic'( 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ] )
% 1.39/1.82 , clause( 1426, [ 'c_Wellfounded_Oacyclic'( 'c_Relation_Oconverse'( X, Y, Y
% 1.39/1.82 ), Y ), ~( 'c_Wellfounded_Oacyclic'( X, Y ) ) ] )
% 1.39/1.82 , clause( 1427, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1428, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.39/1.82 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.39/1.82 , clause( 1429, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1430, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.39/1.82 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.39/1.82 , clause( 1431, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.39/1.82 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.39/1.82 , clause( 1432, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.39/1.82 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 1.39/1.82 , clause( 1433, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetprod'(
% 1.39/1.82 Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( U,
% 1.39/1.82 'tc_bool' ) ), U, X ) ), 'c_Finite__Set_Osetprod'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( U,
% 1.39/1.82 'tc_bool' ) ), U, X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.82 'c_Finite__Set_Osetprod'( Y, Z, U, X ) ), 'c_Finite__Set_Osetprod'( Y, T
% 1.39/1.82 , U, X ) ) ), ~( 'c_Finite__Set_Ofinite'( T, U ) ), ~(
% 1.39/1.82 'c_Finite__Set_Ofinite'( Z, U ) ) ] )
% 1.39/1.82 , clause( 1434, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ), X ) ) ] )
% 1.39/1.82 , clause( 1435, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z )
% 1.39/1.82 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1436, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), ~(
% 1.39/1.82 =( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) )
% 1.39/1.82 ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ), ~( 'c_Finite__Set_Ofinite'( Y
% 1.39/1.82 , T ) ), =( 'c_Finite__Set_Osetprod'( U,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), T, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.82 'c_Finite__Set_Osetprod'( U, Y, T, X ) ), 'c_Finite__Set_Osetprod'( U, Z
% 1.39/1.82 , T, X ) ) ) ] )
% 1.39/1.82 , clause( 1437, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ), Y ) ] )
% 1.39/1.82 , clause( 1438, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~(
% 1.39/1.82 'c_lessequals'( Z, Y, X ) ) ] )
% 1.39/1.82 , clause( 1439, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, X ) ] )
% 1.39/1.82 , clause( 1440, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~(
% 1.39/1.82 'c_lessequals'( Y, Z, X ) ) ] )
% 1.39/1.82 , clause( 1441, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), Y ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1442, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), X ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1443, [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 1.39/1.82 , 'tc_fun'( Z, 'tc_bool' ) ), Y ) ), 'c_lessequals'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1444, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.82 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1445, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ] )
% 1.39/1.82 , clause( 1446, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1447, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ] )
% 1.39/1.82 , clause( 1448, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1449, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z
% 1.39/1.82 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1450, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.39/1.82 ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ), X ), ~(
% 1.39/1.82 'c_lessequals'( U, Z, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), U ) )
% 1.39/1.82 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1451, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( T, U, 'tc_fun'( Y,
% 1.39/1.82 'tc_bool' ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ) ), hAPP( hAPP(
% 1.39/1.82 'c_Finite__Set_Osetsum'( Y, X ), Z ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( T, U, 'tc_fun'( Y,
% 1.39/1.82 'tc_bool' ) ) ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ), ~(
% 1.39/1.82 'c_Finite__Set_Ofinite'( T, Y ) ) ] )
% 1.39/1.82 , clause( 1452, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.39/1.82 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ] )
% 1.39/1.82 , clause( 1453, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.39/1.82 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ] )
% 1.39/1.82 , clause( 1454, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.39/1.82 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ] )
% 1.39/1.82 , clause( 1455, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.39/1.82 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ] )
% 1.39/1.82 , clause( 1456, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.39/1.82 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), X ) ] )
% 1.39/1.82 , clause( 1457, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.39/1.82 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Z ), X ) ] )
% 1.39/1.82 , clause( 1458, [ ~(
% 1.39/1.82 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.39/1.82 'c_lessequals'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1459, [ ~(
% 1.39/1.82 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 1.39/1.82 , clause( 1460, [ ~(
% 1.39/1.82 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.39/1.82 'c_lessequals'( Z, T, X ) ) ] )
% 1.39/1.82 , clause( 1461, [ ~(
% 1.39/1.82 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1462, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 1.39/1.82 ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.39/1.82 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.39/1.82 'c_lessequals'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1463, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 1.39/1.82 ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.39/1.82 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.39/1.82 'c_lessequals'( Z, T, X ) ) ] )
% 1.39/1.82 , clause( 1464, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ] )
% 1.39/1.82 , clause( 1465, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1466, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 X ), Y ) ), Z ) ) ] )
% 1.39/1.82 , clause( 1467, [ =( 'c_Finite__Set_Ocard'( 'c_Set_Oinsert'( X, Y, Z ), Z )
% 1.39/1.82 , 'c_Finite__Set_Ocard'( Y, Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X )
% 1.39/1.82 , Y ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ] )
% 1.39/1.82 , clause( 1468, [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y )
% 1.39/1.82 , 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.39/1.82 'tc_bool' ) ), ~( 'c_lessequals'( X, 'c_Transitive__Closure_Ortrancl'( Z
% 1.39/1.82 , Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1469, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X )
% 1.39/1.82 , ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.39/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1470, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1471, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T )
% 1.39/1.82 ) ) ] )
% 1.39/1.82 , clause( 1472, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1473, [ 'c_Finite__Set_Ofinite'( 'c_Orderings_Otop__class_Otop'(
% 1.39/1.82 'tc_fun'( X, 'tc_bool' ) ), X ), ~( 'c_Finite__Set_Ofinite'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), X ) ),
% 1.39/1.82 ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.39/1.82 , clause( 1474, [ 'c_Finite__Set_Ofinite'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), X ), ~(
% 1.39/1.82 'c_Finite__Set_Ofinite'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), X ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.39/1.82 , clause( 1475, [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.39/1.82 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1476, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.39/1.82 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1477, [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.39/1.82 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1478, [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.39/1.82 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.39/1.82 ) ), 'tc_fun'( X, 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1479, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 1.39/1.82 , clause( 1480, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 1.39/1.82 , =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ] )
% 1.39/1.82 , clause( 1481, [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ] )
% 1.39/1.82 , clause( 1482, [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.39/1.82 X ) ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ) ] )
% 1.39/1.82 , clause( 1483, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.39/1.82 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ) ] )
% 1.39/1.82 , clause( 1484, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1485, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.39/1.82 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1486, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.82 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.82 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.39/1.82 'c_lessequals'( Z, U, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.39/1.82 , clause( 1487, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.82 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.82 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ),
% 1.39/1.82 ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1488, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.39/1.82 X ) ] )
% 1.39/1.82 , clause( 1489, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Set_Oinsert'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X )
% 1.39/1.82 , T ) ) ) ] )
% 1.39/1.82 , clause( 1490, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.39/1.82 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'(
% 1.39/1.82 Y, 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1491, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ] )
% 1.39/1.82 , clause( 1492, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ] )
% 1.39/1.82 , clause( 1493, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ] )
% 1.39/1.82 , clause( 1494, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ] )
% 1.39/1.82 , clause( 1495, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), X ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1496, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1497, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~(
% 1.39/1.82 'c_lessequals'( Y, Z, X ) ) ] )
% 1.39/1.82 , clause( 1498, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, X ) ] )
% 1.39/1.82 , clause( 1499, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~(
% 1.39/1.82 'c_lessequals'( Z, Y, X ) ) ] )
% 1.39/1.82 , clause( 1500, [ 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1501, [ 'c_lessequals'( X,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1502, [ 'c_lessequals'( X,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1503, [ 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1504, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.82 T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1505, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X
% 1.39/1.82 ), X ) ] )
% 1.39/1.82 , clause( 1506, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X
% 1.39/1.82 ), X ) ] )
% 1.39/1.82 , clause( 1507, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.82 T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1508, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.82 T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1509, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ] )
% 1.39/1.82 , clause( 1510, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ] )
% 1.39/1.82 , clause( 1511, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1512, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ] )
% 1.39/1.82 , clause( 1513, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ] )
% 1.39/1.82 , clause( 1514, [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_Wellfounded_Owf'(
% 1.39/1.82 X, Y ) ) ] )
% 1.39/1.82 , clause( 1515, [ 'c_lessequals'( 'c_Relation_OImage'( X, 'c_Set_Oinsert'(
% 1.39/1.82 Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z
% 1.39/1.82 ), 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z
% 1.39/1.82 ) ), 'c_Pair'( Y, T, Z, Z ) ), X ) ) ), ~( 'c_Equiv__Relations_Oequiv'(
% 1.39/1.82 U, X, Z ) ) ] )
% 1.39/1.82 , clause( 1516, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), T ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U ) ) ] )
% 1.39/1.82 , clause( 1517, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), X ) ] )
% 1.39/1.82 , clause( 1518, [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.39/1.82 'c_Transitive__Closure_Ortrancl'( Z, Y ) ), ~( 'c_lessequals'( X,
% 1.39/1.82 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.39/1.82 'tc_bool' ) ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1519, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.82 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1520, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ) ] )
% 1.39/1.82 , clause( 1521, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1522, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.82 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1523, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( X ) ) ), ~( =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( X ) ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ] )
% 1.39/1.82 , clause( 1524, [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( Y, 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X
% 1.39/1.82 , Z ) ] )
% 1.39/1.82 , clause( 1525, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( T, X, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1526, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.39/1.82 , X ) ) ] )
% 1.39/1.82 , clause( 1527, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( Y, Z, X ) ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( T, Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 'tc_nat' ) ), Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.82 , Y, X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T
% 1.39/1.82 ) ) ) ] )
% 1.39/1.82 , clause( 1528, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.39/1.82 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ) ) ), =( Y, Z ) ] )
% 1.39/1.82 , clause( 1529, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 1.39/1.82 , clause( 1530, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 1.39/1.82 , clause( 1531, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.39/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1532, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.39/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1533, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Y,
% 1.39/1.82 'tc_fun'( X, 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1534, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), X ), 'tc_fun'(
% 1.39/1.82 Y, 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool'
% 1.39/1.82 ) ) ) ] )
% 1.39/1.82 , clause( 1535, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( X ) ) ] )
% 1.39/1.82 , clause( 1536, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( X ) ) ] )
% 1.39/1.82 , clause( 1537, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1538, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1539, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1540, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_in'( Z ), X ), Y ) ) ] )
% 1.39/1.82 , clause( 1541, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.39/1.82 , 'tc_nat' ) ] )
% 1.39/1.82 , clause( 1542, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.39/1.82 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.82 X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1543, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.39/1.82 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.82 X ), Y ), Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.39/1.82 , X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.39/1.82 , clause( 1544, [ =( 'c_Set_Ovimage'( X, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), Z ), T, Y ),
% 1.39/1.82 hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( T, 'tc_bool' ) ),
% 1.39/1.82 'c_Set_Ovimage'( X, Z, T, Y ) ) ) ] )
% 1.39/1.82 , clause( 1545, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.39/1.82 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1546, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.39/1.82 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1547, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.39/1.82 X ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.39/1.82 , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1548, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.39/1.82 X ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.39/1.82 , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1549, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.39/1.82 X ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.39/1.82 , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1550, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.39/1.82 X ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.39/1.82 , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1551, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.39/1.82 X ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.39/1.82 , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1552, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_Set_Oinsert'( Y, T, X ), Z, 'tc_fun'( X, 'tc_bool' ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1553, [ =( 'c_Product__Type_OSigma'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), T, Z, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Product__Type_OSigma'( X, T, Z, U ), 'c_Product__Type_OSigma'( Y, T, Z
% 1.39/1.82 , U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1554, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL(
% 1.39/1.82 hAPP( Y, T ) ) ) ] )
% 1.39/1.82 , clause( 1555, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.39/1.82 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 1.39/1.82 , clause( 1556, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 1.39/1.82 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 1.39/1.82 , clause( 1557, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 1.39/1.82 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 1.39/1.82 , clause( 1558, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 1.39/1.82 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ] )
% 1.39/1.82 , clause( 1559, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 1.39/1.82 T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 1.39/1.82 hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ] )
% 1.39/1.82 , clause( 1560, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_in'( Z ), T ), X ) ), ~( 'c_lessequals'( X,
% 1.39/1.82 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1561, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 1.39/1.82 T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 1.39/1.82 hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ] )
% 1.39/1.82 , clause( 1562, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.39/1.82 'c_lessequals'( X, 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) )
% 1.39/1.82 ), hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), X ) ) ] )
% 1.39/1.82 , clause( 1563, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1564, [ 'c_lessequals'( 'c_Set_Ovimage'( X, Y, Z, T ),
% 1.39/1.82 'c_Set_Ovimage'( X, U, Z, T ), 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.39/1.82 'c_lessequals'( Y, U, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1565, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.39/1.82 ), Y ) ] )
% 1.39/1.82 , clause( 1566, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.39/1.82 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ] )
% 1.39/1.82 , clause( 1567, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ] )
% 1.39/1.82 , clause( 1568, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.82 Y, X ), ~( 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1569, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.82 Z, X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1570, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1571, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.82 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1572, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.39/1.82 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1573, [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 1.39/1.82 , 'tc_fun'( Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 1.39/1.82 , 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1574, [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 1.39/1.82 , 'tc_fun'( Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 1.39/1.82 , 'tc_bool' ) ) ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1575, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.39/1.82 , clause( 1576, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.39/1.82 , clause( 1577, [ ~( =( 'c_Finite__Set_Ocard'( X, Y ),
% 1.39/1.82 'c_Finite__Set_Ocard'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.39/1.82 'tc_bool' ) ), Y ) ) ), ~( 'c_Finite__Set_Ofinite'(
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ), =( X,
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1578, [ =( 'c_Relation_Orel__comp'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 1.39/1.82 Z, T ), 'tc_bool' ) ), U, Z, T, W ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 1.39/1.82 , U, Z, T, W ), 'c_Relation_Orel__comp'( Y, U, Z, T, W ), 'tc_fun'(
% 1.39/1.82 'tc_prod'( Z, W ), 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1579, [ =( 'c_Relation_Orel__comp'( X,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 'tc_prod'(
% 1.39/1.82 T, U ), 'tc_bool' ) ), W, T, U ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 1.39/1.82 , Y, W, T, U ), 'c_Relation_Orel__comp'( X, Z, W, T, U ), 'tc_fun'(
% 1.39/1.82 'tc_prod'( W, U ), 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1580, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.39/1.82 'c_lessequals'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1581, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.39/1.82 'c_lessequals'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1582, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 1.39/1.82 , clause( 1583, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, X ), X ) ) ] )
% 1.39/1.82 , clause( 1584, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.82 T, X ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1585, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.82 T, X ), ~( 'c_lessequals'( Z, T, X ) ) ] )
% 1.39/1.82 , clause( 1586, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 1.39/1.82 , clause( 1587, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, X ), X ) ) ] )
% 1.39/1.82 , clause( 1588, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1589, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.39/1.82 , clause( 1590, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1591, [ ~( 'class_Power_Opower'( X ) ), =(
% 1.39/1.82 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.39/1.82 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 1.39/1.82 , clause( 1592, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 1.39/1.82 , clause( 1593, [ 'c_Relation_Ototal__on'( 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( X, 'tc_bool' ) ), Y, X ) ] )
% 1.39/1.82 , clause( 1594, [ 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( T, U,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.39/1.82 Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z
% 1.39/1.82 , 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1595, [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ),
% 1.39/1.82 Y ), 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Z,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ), U ), T, U ) )
% 1.39/1.82 ) ) ] )
% 1.39/1.82 , clause( 1596, [ =( 'c_Relation_Oconverse'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 1.39/1.82 Z, T ), 'tc_bool' ) ), Z, T ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Oconverse'( X,
% 1.39/1.82 Z, T ), 'c_Relation_Oconverse'( Y, Z, T ), 'tc_fun'( 'tc_prod'( T, Z ),
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1597, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.39/1.82 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.82 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.39/1.82 , clause( 1598, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.39/1.82 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.39/1.82 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.39/1.82 , clause( 1599, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ] )
% 1.39/1.82 , clause( 1600, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ] )
% 1.39/1.82 , clause( 1601, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X
% 1.39/1.82 ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1602, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X
% 1.39/1.82 ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1603, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X
% 1.39/1.82 ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1604, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.82 Z, X ) ] )
% 1.39/1.82 , clause( 1605, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.39/1.82 Y, X ) ] )
% 1.39/1.82 , clause( 1606, [ 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1607, [ 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1608, [ 'c_lessequals'( X,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z,
% 1.39/1.82 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Y, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1609, [ 'c_lessequals'( X,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z,
% 1.39/1.82 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Y, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1610, [ 'c_lessequals'( X, 'c_Orderings_Otop__class_Otop'(
% 1.39/1.82 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1611, [ ~( 'class_Orderings_Otop'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 'c_Orderings_Otop__class_Otop'( X ), X ) ] )
% 1.39/1.82 , clause( 1612, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.39/1.82 'c_HOL_Osgn__class_Osgn'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.82 ), 'c_HOL_Oone__class_Oone'( X ) ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1613, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.39/1.82 'c_HOL_Osgn__class_Osgn'( Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.82 ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1614, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1615, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.39/1.82 , Z, X ), 'c_Power_Opower__class_Opower'( T, U, X ), X ), ~(
% 1.39/1.82 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1616, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.39/1.82 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ), X ) ) ] )
% 1.39/1.82 , clause( 1617, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.82 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ), X ) ) ] )
% 1.39/1.82 , clause( 1618, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ), X ) ) ] )
% 1.39/1.82 , clause( 1619, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ), X ) ) ] )
% 1.39/1.82 , clause( 1620, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.39/1.82 =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1621, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.82 ), Y ) ), Z ) ), Z ) ] )
% 1.39/1.82 , clause( 1622, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1623, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ] )
% 1.39/1.82 , clause( 1624, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ] )
% 1.39/1.82 , clause( 1625, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z,
% 1.39/1.82 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1626, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1627, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ] )
% 1.39/1.82 , clause( 1628, [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'(
% 1.39/1.82 Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ),
% 1.39/1.82 ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ) ] )
% 1.39/1.82 , clause( 1629, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1630, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1631, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.39/1.82 , clause( 1632, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1633, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_Orderings_Obot__class_Obot'( X )
% 1.39/1.82 ), 'c_Orderings_Otop__class_Otop'( X ) ) ] )
% 1.39/1.82 , clause( 1634, [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.39/1.82 ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1635, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ] )
% 1.39/1.82 , clause( 1636, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ] )
% 1.39/1.82 , clause( 1637, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1638, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1639, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1640, [ =( 'c_Relation_OImage'( X,
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 1.39/1.82 'tc_fun'( U, 'tc_bool' ) ) ), ~( 'c_Relation_Osingle__valued'(
% 1.39/1.82 'c_Relation_Oconverse'( X, T, U ), U, T ) ) ] )
% 1.39/1.82 , clause( 1641, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.39/1.82 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.39/1.82 T, X ) ), 'c_Power_Opower__class_Opower'( Z, T, X ) ) ), =( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1642, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( Y, Z, X ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Power_Opower__class_Opower'( Y
% 1.39/1.82 , Z, X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ) ] )
% 1.39/1.82 , clause( 1643, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1644, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~(
% 1.39/1.82 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.39/1.82 'c_lessequals'( T, Y, X ) ) ] )
% 1.39/1.82 , clause( 1645, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.39/1.82 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.39/1.82 'c_lessequals'( T, Z, X ) ) ] )
% 1.39/1.82 , clause( 1646, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.39/1.82 'c_lessequals'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1647, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.39/1.82 'c_lessequals'( Z, T, X ) ) ] )
% 1.39/1.82 , clause( 1648, [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.39/1.82 'c_lessequals'( Z, T, X ) ) ] )
% 1.39/1.82 , clause( 1649, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.39/1.82 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), Y ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1650, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.39/1.82 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1651, [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ),
% 1.39/1.82 'c_Finite__Set_Ofinite'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), X ) ] )
% 1.39/1.82 , clause( 1652, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1653, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1654, [ =( 'c_Relation_ORange'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 1.39/1.82 Z, T ), 'tc_bool' ) ), Z, T ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_ORange'( X, Z,
% 1.39/1.82 T ), 'c_Relation_ORange'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1655, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 1.39/1.82 , clause( 1656, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1657, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1658, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~( hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.82 , ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.39/1.82 , Y ), T ), X ) ) ] )
% 1.39/1.82 , clause( 1659, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1660, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ] )
% 1.39/1.82 , clause( 1661, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X,
% 1.39/1.82 'tc_fun'( Y, 'tc_bool' ) ), X ) ] )
% 1.39/1.82 , clause( 1662, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), T ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.39/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ] )
% 1.39/1.82 , clause( 1663, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1664, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.82 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1665, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ] )
% 1.39/1.82 , clause( 1666, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.39/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ] )
% 1.39/1.82 , clause( 1667, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.82 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1668, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, X ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1669, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1670, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X
% 1.39/1.82 ), X ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1671, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X
% 1.39/1.82 ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.39/1.82 , clause( 1672, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, X ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1673, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1674, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, T,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1675, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T, X,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1676, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 1.39/1.82 Y, Z, X ), X ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.39/1.82 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1677, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 1.39/1.82 , X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1678, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.39/1.82 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 1.39/1.82 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1679, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.39/1.82 , Z, X ), T, X ), ~( 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.39/1.82 , U, X ), T, X ) ) ] )
% 1.39/1.82 , clause( 1680, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 1.39/1.82 , Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1681, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 1.39/1.82 , clause( 1682, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y
% 1.39/1.82 , 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 1.39/1.82 , clause( 1683, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 1.39/1.82 , clause( 1684, [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1685, [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1686, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.39/1.82 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.39/1.82 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1687, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( Z, Y ) ) ), ~(
% 1.39/1.82 'c_lessequals'( Z, X, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1688, [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_lessequals'( X, Z,
% 1.39/1.82 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Z,
% 1.39/1.82 Y ) ) ] )
% 1.39/1.82 , clause( 1689, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y
% 1.39/1.82 , X ) ] )
% 1.39/1.82 , clause( 1690, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 1.39/1.82 , Y, X ) ] )
% 1.39/1.82 , clause( 1691, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.39/1.82 , clause( 1692, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), =( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1693, [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1694, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1695, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1696, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1697, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.82 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1698, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.82 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1699, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.82 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1700, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), T ) ), =( T,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1701, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), Z ) ), =( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1702, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , =( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ) ] )
% 1.39/1.82 , clause( 1703, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1704, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ] )
% 1.39/1.82 , clause( 1705, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ] )
% 1.39/1.82 , clause( 1706, [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z,
% 1.39/1.82 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.39/1.82 X, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1707, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1708, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1709, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.39/1.82 'c_HOL_Oone__class_Oone'( X ) ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1710, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.39/1.82 'c_HOL_Oone__class_Oone'( X ) ) ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1711, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.39/1.82 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ] )
% 1.39/1.82 , clause( 1712, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.39/1.82 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.39/1.82 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1713, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.39/1.82 =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( T, Z, X ) ) ), =( Y, T ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 'tc_nat' ) ), Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.82 , T, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1714, [ =( 'c_Relation_ODomain'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 1.39/1.82 Z, T ), 'tc_bool' ) ), Z, T ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_ODomain'( X, Z
% 1.39/1.82 , T ), 'c_Relation_ODomain'( Y, Z, T ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1715, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), T ) ) ] )
% 1.39/1.82 , clause( 1716, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), =( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1717, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), =( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1718, [ =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1719, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.39/1.82 , clause( 1720, [ 'c_lessequals'( 'c_Wellfounded_Oacc'( X, Y ),
% 1.39/1.82 'c_Wellfounded_Oacc'( Z, Y ), 'tc_fun'( Y, 'tc_bool' ) ), ~(
% 1.39/1.82 'c_lessequals'( Z, X, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1721, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1722, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ] )
% 1.39/1.82 , clause( 1723, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ] )
% 1.39/1.82 , clause( 1724, [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z,
% 1.39/1.82 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.39/1.82 X, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1725, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1726, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1727, [ 'c_lessequals'( 'c_Finite__Set_Ocard'( X, Y ),
% 1.39/1.82 'c_Finite__Set_Ocard'( Z, Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Z,
% 1.39/1.82 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ] )
% 1.39/1.82 , clause( 1728, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ] )
% 1.39/1.82 , clause( 1729, [ =( 'c_Set_Ovimage'( X,
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), U, T ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Set_Ovimage'( X, Y, U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U
% 1.39/1.82 , 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1730, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Power_Opower__class_Opower'( Y
% 1.39/1.82 , Z, X ) ) ), 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ), ~( hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.39/1.82 X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.39/1.82 , clause( 1731, [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.39/1.82 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Finite__Set_Ocard'(
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1732, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.82 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1'( X, Z, T ) ) )
% 1.39/1.82 ), ~( 'c_Wellfounded_Owf'( Z, T ) ) ] )
% 1.39/1.82 , clause( 1733, [ =( 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.39/1.82 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.39/1.82 'tc_bool' ) ), Y ), 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 1.39/1.82 Y, Y ), 'tc_bool' ) ), Y ) ) ] )
% 1.39/1.82 , clause( 1734, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), T ) ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1735, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), T ) ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1736, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Y ) ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ] )
% 1.39/1.82 , clause( 1737, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Y ) ) ), ~( hBOOL(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ] )
% 1.39/1.82 , clause( 1738, [ =( 'c_Finite__Set_Ocard'( 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( X, 'tc_bool' ) ), X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1739, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.39/1.82 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Osgn__class_Osgn'( Y, X ), X ),
% 1.39/1.82 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ] )
% 1.39/1.82 , clause( 1740, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.39/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Finite__Set_Ocard'( X, Y )
% 1.39/1.82 ) ), ~( 'c_Finite__Set_Ofinite'( X, Y ) ), =( X,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1741, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.39/1.82 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1742, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.39/1.82 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.39/1.82 , clause( 1743, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ] )
% 1.39/1.82 , clause( 1744, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ] )
% 1.39/1.82 , clause( 1745, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ] )
% 1.39/1.82 , clause( 1746, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), Y ) ) ) ] )
% 1.39/1.82 , clause( 1747, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), Y ) ) ) ] )
% 1.39/1.82 , clause( 1748, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1749, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.82 X ), Y ), T ) ), Z ) ) ] )
% 1.39/1.82 , clause( 1750, [ =( 'c_Relation_ORange'( 'c_Set_Oinsert'( 'c_Pair'( X, Y,
% 1.39/1.82 Z, T ), U, 'tc_prod'( Z, T ) ), Z, T ), 'c_Set_Oinsert'( Y,
% 1.39/1.82 'c_Relation_ORange'( U, Z, T ), T ) ) ] )
% 1.39/1.82 , clause( 1751, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ) ), ~( 'c_lessequals'( X, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Z, 'tc_bool' ) ), Y ), 'tc_fun'(
% 1.39/1.82 Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1752, [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y
% 1.39/1.82 , 'tc_fun'( Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 1.39/1.82 , 'tc_bool' ) ) ) ), 'c_lessequals'( X, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Z, 'tc_bool' ) ), Y ), 'tc_fun'(
% 1.39/1.82 Z, 'tc_bool' ) ) ] )
% 1.39/1.82 , clause( 1753, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1754, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ] )
% 1.39/1.82 , clause( 1755, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y ) ] )
% 1.39/1.82 , clause( 1756, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ) ), Y ), Y ) ] )
% 1.39/1.82 , clause( 1757, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.39/1.82 'class_Int_Onumber__ring'( X ) ), =( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1758, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 1.39/1.82 , clause( 1759, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.39/1.82 , Y ), Y ) ] )
% 1.39/1.82 , clause( 1760, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ), Y ) ] )
% 1.39/1.82 , clause( 1761, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 1.39/1.82 , clause( 1762, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y ) ] )
% 1.39/1.82 , clause( 1763, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.82 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.82 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ) ) ] )
% 1.39/1.82 , clause( 1764, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.39/1.82 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.39/1.82 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.39/1.82 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.39/1.82 ), Y ), T ), Z, X ) ) ] )
% 1.39/1.82 , clause( 1765, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.39/1.82 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ] )
% 1.39/1.82 , clause( 1766, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( 'c_lessequals'( Y, hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1767, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.39/1.82 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), T ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1768, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), hBOOL( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ] )
% 1.39/1.82 , clause( 1769, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1770, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.39/1.82 ~( =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y ) ), =( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1771, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1772, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Z ), Y ), X ) ) ] )
% 1.39/1.82 , clause( 1773, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Z ), X ) ) ] )
% 1.39/1.82 , clause( 1774, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Z ), Y ), X ) ) ] )
% 1.39/1.82 , clause( 1775, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.82 X ), Y ), Z ) ), Z ), Y ) ] )
% 1.39/1.82 , clause( 1776, [ ~( =( hAPP( X, 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X
% 1.39/1.82 , Y, Z, T, U, W ) ), hAPP( Y, 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X,
% 1.39/1.82 Y, Z, T, U, W ) ) ) ), =( 'c_Recdef_Ocut'( X, Z, T, U, W ),
% 1.39/1.82 'c_Recdef_Ocut'( Y, Z, T, U, W ) ) ] )
% 1.39/1.82 , clause( 1777, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.39/1.82 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.39/1.82 T, Z, X ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Oone__class_Oone'( X ) ), T ) ) ) ] )
% 1.39/1.82 , clause( 1778, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.39/1.82 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.39/1.82 T, Z, X ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Oone__class_Oone'( X ) ), T ) ) ) ] )
% 1.39/1.82 , clause( 1779, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T,
% 1.39/1.82 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.82 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ) ] )
% 1.39/1.82 , clause( 1780, [ 'c_Relation_Osingle__valued'( 'c_Relation_OId__on'( X, Y
% 1.39/1.82 ), Y, Y ) ] )
% 1.39/1.82 , clause( 1781, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ] )
% 1.39/1.82 , clause( 1782, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ) ] )
% 1.39/1.82 , clause( 1783, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ] )
% 1.39/1.82 , clause( 1784, [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), Y ) ), Y ) ] )
% 1.39/1.82 , clause( 1785, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 X ), Y ) ), Y ) ] )
% 1.39/1.82 , clause( 1786, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 X ), Y ) ), Y ) ] )
% 1.39/1.82 , clause( 1787, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 X ), Y ) ) ) ] )
% 1.39/1.82 , clause( 1788, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 X ), Y ) ) ) ] )
% 1.39/1.82 , clause( 1789, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 X ), Y ) ), Y ) ] )
% 1.39/1.82 , clause( 1790, [ 'c_Wellfounded_Oacyclic'( X, Y ), ~(
% 1.39/1.82 'c_Wellfounded_Oacyclic'( 'c_Set_Oinsert'( 'c_Pair'( Z, T, Y, Y ), X,
% 1.39/1.82 'tc_prod'( Y, Y ) ), Y ) ) ] )
% 1.39/1.82 , clause( 1791, [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'(
% 1.39/1.82 Z, Y ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool'
% 1.39/1.82 ) ) ) ] )
% 1.39/1.82 , clause( 1792, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.39/1.82 'c_Finite__Set_Ofinite'( Z, Y ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( Y,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1793, [ hBOOL( hAPP( X, Y ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'(
% 1.39/1.82 T, 'tc_bool' ) ) ), ~( hBOOL( hAPP( Z, Y ) ) ) ] )
% 1.39/1.82 , clause( 1794, [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_lessequals'( X, Z
% 1.39/1.82 , 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ), ~(
% 1.39/1.82 'c_Wellfounded_Oacyclic'( Z, Y ) ) ] )
% 1.39/1.82 , clause( 1795, [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_lessequals'( X, Z
% 1.39/1.82 , 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ] )
% 1.39/1.82 , clause( 1796, [ 'c_Relation_Osingle__valued'( X, Y, Z ), ~(
% 1.39/1.82 'c_Relation_Osingle__valued'( T, Y, Z ) ), ~( 'c_lessequals'( X, T,
% 1.39/1.82 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1797, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.82 , 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T
% 1.39/1.82 ), X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ] )
% 1.39/1.82 , clause( 1798, [ ~( =( 'c_Finite__Set_Ocard'( X, Y ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_Finite__Set_Ofinite'( X
% 1.39/1.82 , Y ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1799, [ 'c_lessequals'(
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.82 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( T, U,
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.39/1.82 Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z
% 1.39/1.82 , 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1800, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.39/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.82 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1801, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.39/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.39/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.82 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1802, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 1.39/1.82 , =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ] )
% 1.39/1.82 , clause( 1803, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ] )
% 1.39/1.82 , clause( 1804, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.82 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.39/1.82 , clause( 1805, [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.39/1.82 'tc_bool' ) ) ), ~( 'c_lessequals'( X, hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), X ), 'tc_fun'(
% 1.39/1.82 Y, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1806, [ 'c_lessequals'( 'c_Relation_ODomain'( X, Y, Z ),
% 1.39/1.82 'c_Relation_ODomain'( T, Y, Z ), 'tc_fun'( Y, 'tc_bool' ) ), ~(
% 1.39/1.82 'c_lessequals'( X, T, 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1807, [ =( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), =( X, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.39/1.82 Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1808, [ =( 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Y, Z, T ), U, T )
% 1.39/1.82 , 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Ovimage'( X,
% 1.39/1.82 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.39/1.82 'tc_bool' ) ), T ), U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U,
% 1.39/1.82 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1809, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.39/1.82 )
% 1.39/1.82 , clause( 1810, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.82 ) ) ) ] )
% 1.39/1.82 , clause( 1811, [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.82 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~(
% 1.39/1.82 hBOOL( hAPP( X, T ) ) ) ] )
% 1.39/1.82 , clause( 1812, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.82 , =( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.39/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ) ] )
% 1.39/1.82 , clause( 1813, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.82 , ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( U
% 1.39/1.82 , T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 1.39/1.82 , clause( 1814, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.82 , ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( Z
% 1.39/1.82 , Y, X ), ~( 'c_lessequals'( U, T, X ) ) ] )
% 1.39/1.82 , clause( 1815, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.82 'c_Power_Opower__class_Opower'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.82 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( Y, T, X ) ),
% 1.39/1.82 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ] )
% 1.39/1.82 , clause( 1816, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.82 =( 'c_Power_Opower__class_Opower'( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( Y, T,
% 1.39/1.82 X ) ), 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ] )
% 1.39/1.82 , clause( 1817, [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ),
% 1.39/1.82 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.39/1.82 Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1818, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.39/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( X,
% 1.39/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.39/1.82 ) ] )
% 1.39/1.82 , clause( 1819, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.39/1.82 X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), W ) ) ), T
% 1.39/1.82 ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ] )
% 1.39/1.82 , clause( 1820, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.39/1.82 X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), W
% 1.39/1.82 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), W ), X ) ), ~(
% 1.39/1.82 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ] )
% 1.39/1.82 , clause( 1821, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.82 ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), U ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ] )
% 1.39/1.82 , clause( 1822, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), =( U,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.82 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ] )
% 1.39/1.82 , clause( 1823, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z
% 1.39/1.82 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1824, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.39/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1825, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.39/1.82 'c_HOL_Osgn__class_Osgn'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.82 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.82 'c_HOL_Osgn__class_Osgn'( Y, X ) ), 'c_HOL_Osgn__class_Osgn'( Z, X ) ) )
% 1.39/1.82 ] )
% 1.39/1.82 , clause( 1826, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.39/1.82 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1827, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1828, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1829, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.82 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ] )
% 1.39/1.82 , clause( 1830, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1831, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.39/1.82 , clause( 1832, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.39/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.39/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.82 , clause( 1833, [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( Y, 'tc_bool' ) ), Z, Y ), 'c_Orderings_Obot__class_Obot'(
% 1.39/1.82 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1834, [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.39/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.82 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ] )
% 1.39/1.82 , clause( 1835, [ 'c_lessequals'( 'c_Relation_OImage'( X, Y, Z, T ),
% 1.39/1.82 'c_Relation_OImage'( U, W, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 1.39/1.82 'c_lessequals'( Y, W, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.39/1.82 , U, 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ) ) ] )
% 1.39/1.82 , clause( 1836, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.39/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.39/1.82 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.82 , clause( 1837, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ] )
% 1.39/1.83 , clause( 1838, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.83 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ] )
% 1.39/1.83 , clause( 1839, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.83 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ] )
% 1.39/1.83 , clause( 1840, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.83 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ] )
% 1.39/1.83 , clause( 1841, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.83 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ] )
% 1.39/1.83 , clause( 1842, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.83 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ] )
% 1.39/1.83 , clause( 1843, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.83 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.83 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 1844, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.83 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 1845, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.83 =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.83 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 1846, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.83 ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ] )
% 1.39/1.83 , clause( 1847, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.39/1.83 ), Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ] )
% 1.39/1.83 , clause( 1848, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), ~( 'c_lessequals'( U
% 1.39/1.83 , Z, X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( 'c_lessequals'(
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.39/1.83 , clause( 1849, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 1.39/1.83 'tc_nat' ) ] )
% 1.39/1.83 , clause( 1850, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.39/1.83 , Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 1.39/1.83 , clause( 1851, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.39/1.83 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( X, Y ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( Z ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 'tc_nat' ) ), 'c_Finite__Set_Osetprod'( X, T, Z, 'tc_nat' ) ) ) ), ~(
% 1.39/1.83 'c_Finite__Set_Ofinite'( T, Z ) ) ] )
% 1.39/1.83 , clause( 1852, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Oone__class_Oone'( X ) ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.39/1.83 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 1853, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ), 'c_Set_Oinsert'( T, U,
% 1.39/1.83 Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Z, T ) ), hAPP(
% 1.39/1.83 hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( Y ), T ), U ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ] )
% 1.39/1.83 , clause( 1854, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( Y, 'c_Set_Oinsert'( Z, T, U ), U, X ), hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, Z ) ),
% 1.39/1.83 'c_Finite__Set_Osetprod'( Y, T, U, X ) ) ), hBOOL( hAPP( hAPP( 'c_in'( U
% 1.39/1.83 ), Z ), T ) ), ~( 'c_Finite__Set_Ofinite'( T, U ) ) ] )
% 1.39/1.83 , clause( 1855, [ 'c_Wellfounded_Oacyclic'( 'c_Set_Oinsert'( 'c_Pair'( X, Y
% 1.39/1.83 , Z, Z ), T, 'tc_prod'( Z, Z ) ), Z ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, X, Z, Z ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( T, Z ) ) ), ~( 'c_Wellfounded_Oacyclic'(
% 1.39/1.83 T, Z ) ) ] )
% 1.39/1.83 , clause( 1856, [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.83 'c_Pair'( Y, Z, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) )
% 1.39/1.83 , ~( 'c_Wellfounded_Oacyclic'( 'c_Set_Oinsert'( 'c_Pair'( Z, Y, X, X ), T
% 1.39/1.83 , 'tc_prod'( X, X ) ), X ) ) ] )
% 1.39/1.83 , clause( 1857, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'(
% 1.39/1.83 X, T, U, Z ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 1.39/1.83 X, T, U, Z ), Z, Z ) ), U ) ), ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ) ) ] )
% 1.39/1.83 , clause( 1858, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, T,
% 1.39/1.83 U, Z ), 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2'(
% 1.39/1.83 X, T, U, Z ), Z, Z ) ), U ) ), ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( T, Y, Z, Z ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ) ) ] )
% 1.39/1.83 , clause( 1859, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_OImage'(
% 1.39/1.83 Z, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.39/1.83 'tc_bool' ) ), X ), X, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T
% 1.39/1.83 ) ) ), ~( 'c_Equiv__Relations_Oequiv'( T, Z, X ) ) ] )
% 1.39/1.83 , clause( 1860, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), U ),
% 1.39/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Relation_OImage'( T,
% 1.39/1.83 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.39/1.83 'tc_bool' ) ), X ), X, X ), 'c_Relation_OImage'( T, 'c_Set_Oinsert'( Z,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X, X ),
% 1.39/1.83 'tc_fun'( X, 'tc_bool' ) ) ) ) ), ~( 'c_Equiv__Relations_Oequiv'( W, T, X
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 1861, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), U ) ) ),
% 1.39/1.83 ~( 'c_lessequals'( 'c_Relation_OImage'( T, 'c_Set_Oinsert'( Z,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X, X ),
% 1.39/1.83 'c_Relation_OImage'( T, 'c_Set_Oinsert'( Y,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X, X ),
% 1.39/1.83 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, T, X ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 1862, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.83 X ), Y ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 1863, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ] )
% 1.39/1.83 , clause( 1864, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 1865, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.83 T ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 1866, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ] )
% 1.39/1.83 , clause( 1867, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 1868, [ ~(
% 1.39/1.83 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 1869, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 1870, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 1871, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.83 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 1872, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 1873, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 1874, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 1875, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.83 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 1876, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 1877, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 1878, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 1879, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 1880, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 1881, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ] )
% 1.39/1.83 , clause( 1882, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ] )
% 1.39/1.83 , clause( 1883, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.83 ) ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 1884, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.83 ) ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 1885, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.39/1.83 Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 1886, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.83 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 1887, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 1888, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 1889, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 1890, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 1891, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ] )
% 1.39/1.83 , clause( 1892, [ ~(
% 1.39/1.83 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( 'c_lessequals'( Y, T, X
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 1893, [ ~(
% 1.39/1.83 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( 'c_lessequals'( Z, U, X
% 1.39/1.83 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 1894, [ =( 'c_Set_Ovimage'( X,
% 1.39/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.39/1.83 'tc_bool' ) ), U, T ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.39/1.83 'c_Set_Ovimage'( X, Y, U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U
% 1.39/1.83 , 'tc_bool' ) ) ) ] )
% 1.39/1.83 , clause( 1895, [ 'c_Finite__Set_Ofinite'(
% 1.39/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.83 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ] )
% 1.39/1.83 , clause( 1896, [ 'c_Finite__Set_Ofinite'(
% 1.39/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.39/1.83 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ) ] )
% 1.39/1.83 , clause( 1897, [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( hAPP( Y, Z )
% 1.39/1.83 , hAPP( T, Z ), X ), ~( 'c_lessequals'( Y, T, 'tc_fun'( U, X ) ) ) ] )
% 1.39/1.83 , clause( 1898, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X )
% 1.39/1.83 , ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 1899, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X )
% 1.39/1.83 , ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 1900, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X )
% 1.39/1.83 , ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 1901, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X )
% 1.39/1.83 , ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 1902, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.39/1.83 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.39/1.83 , clause( 1903, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.39/1.83 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.39/1.83 , clause( 1904, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z,
% 1.39/1.83 T, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.39/1.83 , clause( 1905, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z,
% 1.39/1.83 T, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.39/1.83 , clause( 1906, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'(
% 1.39/1.83 X, 'tc_bool' ) ) ) ] )
% 1.39/1.83 , clause( 1907, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~(
% 1.39/1.83 'c_lessequals'( T, Z, 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( X ), Y ), T ) ) ) ] )
% 1.39/1.83 , clause( 1908, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'(
% 1.39/1.83 X, 'tc_bool' ) ) ) ] )
% 1.39/1.83 , clause( 1909, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'(
% 1.39/1.83 X, 'tc_bool' ) ) ) ] )
% 1.39/1.83 , clause( 1910, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 1.39/1.83 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.39/1.83 , clause( 1911, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 1.39/1.83 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.39/1.83 , clause( 1912, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.39/1.83 , clause( 1913, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.39/1.83 , Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 1914, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.39/1.83 , clause( 1915, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.39/1.83 , clause( 1916, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), =( Y, T ),
% 1.39/1.83 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( T, Z, X ) ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 1917, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( T, Z, 'tc_fun'( X,
% 1.39/1.83 'tc_bool' ) ) ) ) ) ] )
% 1.39/1.83 , clause( 1918, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.83 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ] )
% 1.39/1.83 , clause( 1919, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Z ) ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ] )
% 1.39/1.83 , clause( 1920, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.83 'tc_fun'( X, 'tc_bool' ) ), Z ) ) ) ) ] )
% 1.39/1.83 , clause( 1921, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y,
% 1.39/1.83 Z, X ) ) ) ] )
% 1.39/1.83 , clause( 1922, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y,
% 1.39/1.83 Z, X ) ) ) ] )
% 1.39/1.83 , clause( 1923, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y,
% 1.39/1.83 Z, X ) ) ) ] )
% 1.39/1.83 , clause( 1924, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, 'tc_fun'( X,
% 1.39/1.83 'tc_bool' ) ) ) ) ) ] )
% 1.39/1.83 , clause( 1925, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( X ), Y ),
% 1.39/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.39/1.83 'tc_bool' ) ) ) ) ) ] )
% 1.39/1.83 , clause( 1926, [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 Z ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 1927, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T,
% 1.39/1.83 Z ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( Z ), X ), Y ) ), =( Y, T ) ] )
% 1.39/1.83 , clause( 1928, [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( Z ), X ), Y ) ) ) ] )
% 1.39/1.83 , clause( 1929, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.39/1.83 Y, Z, X ) ) ] )
% 1.39/1.83 , clause( 1930, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 1.39/1.83 'c_lessequals'( Y, Z, X ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.39/1.83 X ), Y ), Z ) ) ] )
% 1.39/1.83 , clause( 1931, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( Y, Z, X )
% 1.39/1.83 ), =( Y, Z ) ] )
% 1.39/1.83 , clause( 1932, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.39/1.83 Y, Z, X ) ) ] )
% 1.39/1.83 , clause( 1933, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.39/1.83 Y, Z, X ) ) ] )
% 1.39/1.83 , clause( 1934, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.39/1.83 Y, Z, X ) ) ] )
% 1.39/1.83 , clause( 1935, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( Y, Z, X )
% 1.39/1.83 ), =( Z, Y ) ] )
% 1.39/1.83 , clause( 1936, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Z, Y ), ~( 'c_lessequals'(
% 1.39/1.83 Y, Z, X ) ) ] )
% 1.39/1.83 , clause( 1937, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), T ), U ) ) ) ] )
% 1.39/1.83 , clause( 1938, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), T ), U ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ] )
% 1.39/1.83 , clause( 1939, [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( T, Z, X )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 1940, [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( 'c_lessequals'( Y, T, X
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 1941, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, X
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 1942, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( 'c_lessequals'( Y, T, X )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 1943, [ ~(
% 1.39/1.83 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ] )
% 1.39/1.83 , clause( 1944, [ ~(
% 1.39/1.83 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ] )
% 1.39/1.83 , clause( 1945, [ ~(
% 1.39/1.83 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ] )
% 1.39/1.83 , clause( 1946, [ ~(
% 1.39/1.83 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ] )
% 1.39/1.83 , clause( 1947, [ ~(
% 1.39/1.83 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.39/1.83 , clause( 1948, [ ~(
% 1.39/1.83 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.39/1.83 , clause( 1949, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 1.39/1.83 , Z, X ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z )
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 1950, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 1.39/1.83 , X ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 1951, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.39/1.83 , clause( 1952, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ] )
% 1.39/1.83 , clause( 1953, [ ~(
% 1.39/1.83 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.39/1.83 , clause( 1954, [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), 'c_lessequals'( Z, Y, X ),
% 1.39/1.83 ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.39/1.83 , clause( 1955, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ] )
% 1.39/1.83 , clause( 1956, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ] )
% 1.39/1.83 , clause( 1957, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), 'c_lessequals'( Z, Y, X ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 1958, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 1.39/1.83 Y, Y, X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Y
% 1.39/1.83 ) ) ) ] )
% 1.39/1.83 , clause( 1959, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 1960, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( 'c_lessequals'( Z
% 1.39/1.83 , Y, X ) ) ] )
% 1.39/1.83 , clause( 1961, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 1.39/1.83 , Z, X ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 1962, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 1.39/1.83 Y, Z, X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y
% 1.39/1.83 ) ) ) ] )
% 1.39/1.83 , clause( 1963, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), 'c_lessequals'( Z, Y, X ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 1964, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'(
% 1.39/1.83 Y, Z, X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y
% 1.39/1.83 ) ) ) ] )
% 1.39/1.83 , clause( 1965, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ] )
% 1.39/1.83 , clause( 1966, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ] )
% 1.39/1.83 , clause( 1967, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ] )
% 1.39/1.83 , clause( 1968, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.39/1.83 , clause( 1969, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.83 X ), Y ) ) ) ) ] )
% 1.39/1.83 , clause( 1970, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.83 X ), Y ) ) ) ) ] )
% 1.39/1.83 , clause( 1971, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.39/1.83 , Z ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 1972, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.39/1.83 , Z ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 1973, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.39/1.83 , X ), Y ) ), =( X, Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.39/1.83 , clause( 1974, [ =( X, Y ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.39/1.83 'tc_nat' ), X ), Y ) ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.39/1.83 , clause( 1975, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.39/1.83 , X ), Y ) ), =( X, Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.39/1.83 , clause( 1976, [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.39/1.83 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 'tc_nat' ) ) ) ) ] )
% 1.39/1.83 , clause( 1977, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.39/1.83 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), =( X,
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.39/1.83 , clause( 1978, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ] )
% 1.39/1.83 , clause( 1979, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ] )
% 1.39/1.83 , clause( 1980, [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.39/1.83 ), X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 1.39/1.83 , clause( 1981, [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.39/1.83 ), X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 1.39/1.83 , clause( 1982, [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.83 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.39/1.83 ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z
% 1.39/1.83 ) ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ) ), ~(
% 1.39/1.83 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ] )
% 1.39/1.83 , clause( 1983, [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.83 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.39/1.83 ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z ) ), X ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( Z ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.39/1.83 , Y ), U ) ) ) ] )
% 1.39/1.83 , clause( 1984, [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.83 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z
% 1.39/1.83 ) ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( Z ), Y ), U ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U
% 1.39/1.83 , X, Z ) ) ] )
% 1.39/1.83 , clause( 1985, [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.83 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( Z ), Y ), U ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z ) )
% 1.39/1.83 , X ) ) ] )
% 1.39/1.83 , clause( 1986, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBS'( 'c_COMBS'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y
% 1.39/1.83 , 'tc_bool' ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X )
% 1.39/1.83 ), Y ), T, Y, X, 'tc_fun'( X, X ) ), U, Y, X, X ) ), W ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y,
% 1.39/1.83 X ), T ), 'c_Lattices_Olower__semilattice__class_Oinf'( W, Z, 'tc_fun'( Y
% 1.39/1.83 , 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), U ),
% 1.39/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( W, hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.39/1.83 Y, 'tc_bool' ) ) ) ) ), ~( 'c_Finite__Set_Ofinite'( W, Y ) ) ] )
% 1.39/1.83 , clause( 1987, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.39/1.83 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 1988, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.39/1.83 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ] )
% 1.39/1.83 , clause( 1989, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.39/1.83 ) ) ) ) ] )
% 1.39/1.83 , clause( 1990, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.39/1.83 ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 1991, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Osgn__class_Osgn'( Y,
% 1.39/1.83 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 1992, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Osgn__class_Osgn'( Y, X ) ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 1993, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 1994, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 1995, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 X ) ) ) ) ] )
% 1.39/1.83 , clause( 1996, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.39/1.83 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 1997, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.83 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 1998, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.39/1.83 , Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 1999, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.83 ) ), 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2000, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.83 ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2001, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 2002, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.39/1.83 ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 2003, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.39/1.83 ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 2004, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 2005, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.83 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ] )
% 1.39/1.83 , clause( 2006, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.83 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2007, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.83 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2008, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 2009, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Power_Opower__class_Opower'( Y, Z,
% 1.39/1.83 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2010, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 1.39/1.83 ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.83 X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2011, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 X ) ) ) ) ] )
% 1.39/1.83 , clause( 2012, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2013, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.83 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2014, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.83 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2015, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 1.39/1.83 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2016, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2017, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 2018, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2019, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2020, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 2021, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ] )
% 1.39/1.83 , clause( 2022, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2023, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ] )
% 1.39/1.83 , clause( 2024, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2025, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.83 X ), Z ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.39/1.83 ) ) ) ] )
% 1.39/1.83 , clause( 2026, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.83 ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ] )
% 1.39/1.83 , clause( 2027, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.83 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.39/1.83 ) ) ) ] )
% 1.39/1.83 , clause( 2028, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.83 ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2029, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.83 X ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 2030, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.39/1.83 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2031, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.39/1.83 X ), Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2032, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2033, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.39/1.83 X ) ) ] )
% 1.39/1.83 , clause( 2034, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.39/1.83 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.83 , clause( 2035, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.39/1.83 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.83 , clause( 2036, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'(
% 1.39/1.83 X ), X ) ] )
% 1.39/1.83 , clause( 2037, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.39/1.83 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 X ), X ) ) ] )
% 1.39/1.83 , clause( 2038, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.39/1.83 'c_HOL_Oone__class_Oone'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.39/1.83 ), =( Y, Z ) ] )
% 1.39/1.83 , clause( 2039, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Oone__class_Oone'( X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.39/1.83 X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Oone__class_Oone'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2040, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2041, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.39/1.83 =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.39/1.83 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.39/1.83 , =( Z, T ) ] )
% 1.39/1.83 , clause( 2042, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, T
% 1.39/1.83 ) ), 'c_Pair'( U, Y, Z, T ) ), W ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( Z, T ) ), 'c_Pair'( U, X, Z, T ) ), W ) ) ), ~(
% 1.39/1.83 'c_Relation_Osingle__valued'( W, Z, T ) ) ] )
% 1.39/1.83 , clause( 2043, [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, T ), U ) ),
% 1.39/1.83 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( W, W ) ), 'c_Pair'( Z, U, W, W )
% 1.39/1.83 ), V0 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( V1, V1 ) ),
% 1.39/1.83 'c_Pair'( Y, T, V1, V1 ) ), V2 ) ) ), ~( 'c_Equiv__Relations_Ocongruent2'(
% 1.39/1.83 V2, V0, X, V1, W, V3 ) ) ] )
% 1.39/1.83 , clause( 2044, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =(
% 1.39/1.83 hAPP( Y, 'c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1'( Z, Y, T,
% 1.39/1.83 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.39/1.83 'c_Finite__Set_Osetsum'( T, X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 2045, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ),
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.83 , clause( 2046, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.39/1.83 hAPP( 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBB'(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), Z, X, X, Y ) ), T ), hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.39/1.83 Y, X ), Z ), T ) ) ) ] )
% 1.39/1.83 , clause( 2047, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.39/1.83 'c_Finite__Set_Osetsum'( Z, X ), T ), U ) ), hAPP( hAPP(
% 1.39/1.83 'c_Finite__Set_Osetsum'( Z, X ), 'c_COMBB'( hAPP(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T, X, X, Z ) ), U ) ) ] )
% 1.39/1.83 , clause( 2048, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), X ) ] )
% 1.39/1.83 , clause( 2049, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), X ) ] )
% 1.39/1.83 , clause( 2050, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.83 , clause( 2051, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.39/1.83 'c_lessequals'( hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z, 'tc_bool' )
% 1.39/1.83 , 'tc_bool' ), X ), hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z,
% 1.39/1.83 'tc_bool' ), 'tc_bool' ), Y ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.39/1.83 , clause( 2052, [ 'c_lessequals'( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'(
% 1.39/1.83 X, 'tc_bool' ), 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X,
% 1.39/1.83 'tc_fun'( X, 'tc_bool' ), 'tc_bool' ), Z ), 'tc_fun'( X, 'tc_bool' ) ),
% 1.39/1.83 ~( 'c_lessequals'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.39/1.83 , clause( 2053, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 Z, T, X, Y ) ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), T ),
% 1.39/1.83 'c_Relation_OImage'( U, 'c_Set_Oinsert'( Z,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X, Y ) )
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 2054, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_OImage'(
% 1.39/1.83 Z, 'c_Set_Oinsert'( T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U,
% 1.39/1.83 'tc_bool' ) ), U ), U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 U, X ) ), 'c_Pair'( T, Y, U, X ) ), Z ) ) ) ] )
% 1.39/1.83 , clause( 2055, [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1'( Y, Z, X ) ), Y
% 1.39/1.83 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Y ) ) ), ~(
% 1.39/1.83 'c_Wellfounded_Owf'( Z, X ) ) ] )
% 1.39/1.83 , clause( 2056, [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1'( Y, Z, X ) ), Y ) ),
% 1.39/1.83 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Y ) ) ), ~( 'c_Wellfounded_Owf'(
% 1.39/1.83 Z, X ) ) ] )
% 1.39/1.83 , clause( 2057, [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_Wellfounded_Owf'(
% 1.39/1.83 'c_Set_Oinsert'( 'c_Pair'( Z, T, Y, Y ), X, 'tc_prod'( Y, Y ) ), Y ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 2058, [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Relation__XImageE__1__1'( Y, Z, T, X, U ) ), Y ) ),
% 1.39/1.83 ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Relation_OImage'( T, Y, X, U )
% 1.39/1.83 ) ) ) ] )
% 1.39/1.83 , clause( 2059, [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1'( Y, Z, T, X, U ) ), Y )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Relation_OImage'( T, Y, X
% 1.39/1.83 , U ) ) ) ) ] )
% 1.39/1.83 , clause( 2060, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( 'tc_prod'(
% 1.39/1.83 X, X ), 'tc_bool' ) ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 X, X ) ), Y ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2061, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( 'tc_prod'(
% 1.39/1.83 X, X ), 'tc_bool' ) ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 X, X ) ), Y ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2062, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), ~(
% 1.39/1.83 =( hAPP( Y, 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1'( Z, Y
% 1.39/1.83 , T, X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ), =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 2063, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 1.39/1.83 , 'tc_bool' ) ), Z, X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 1.39/1.83 , clause( 2064, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( Z, X ) ) ), ~( 'c_lessequals'( T, Z,
% 1.39/1.83 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( X, X ) ), Y ), 'c_Transitive__Closure_Otrancl'( T, X )
% 1.39/1.83 ) ) ) ] )
% 1.39/1.83 , clause( 2065, [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.83 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z
% 1.39/1.83 ) ), X ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ] )
% 1.39/1.83 , clause( 2066, [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 1.39/1.83 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'( Y, T, Z, Z
% 1.39/1.83 ) ), X ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ] )
% 1.39/1.83 , clause( 2067, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, Z, T ) ) ) ),
% 1.39/1.83 ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), 'c_Wellfounded_Oacc'( Z, T ) ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2068, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.83 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, Z ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( Z, 't_a' ) ) ) ) ] )
% 1.39/1.83 , clause( 2069, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, T, Z ) )
% 1.39/1.83 , 'c_Wellfounded_Oacc'( T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y
% 1.39/1.83 ), 'c_Wellfounded_Oacc'( T, Z ) ) ) ) ] )
% 1.39/1.83 , clause( 2070, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1'( Y, Z, X ) ),
% 1.39/1.83 'c_Wellfounded_Oacc'( Y, X ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ),
% 1.39/1.83 'c_Wellfounded_Oacc'( Y, X ) ) ) ] )
% 1.39/1.83 , clause( 2071, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, Z, T ) )
% 1.39/1.83 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), 'c_Wellfounded_Oacc'( Z, T
% 1.39/1.83 ) ) ) ) ] )
% 1.39/1.83 , clause( 2072, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.83 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, Z ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( Z, 't_a' ) ) ) ) ] )
% 1.39/1.83 , clause( 2073, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'(
% 1.39/1.83 Z, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1'( Z, Y, X ) ),
% 1.39/1.83 'c_Wellfounded_Oacc'( Z, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2074, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, T, Z ) ),
% 1.39/1.83 'c_Wellfounded_Oacc'( T, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y )
% 1.39/1.83 , 'c_Wellfounded_Oacc'( T, Z ) ) ) ) ] )
% 1.39/1.83 , clause( 2075, [ 'c_Wellfounded_Owf'(
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 1.39/1.83 , X, Y, Y, Y ), 'c_Relation_Orel__comp'( Z, X, Y, Y, Y ), 'tc_fun'(
% 1.39/1.83 'tc_prod'( Y, Y ), 'tc_bool' ) ), Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 1.39/1.83 'tc_bool' ) ), Y ), ~( 'c_Wellfounded_Owf'(
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 1.39/1.83 Y, Y ), 'tc_bool' ) ), Y ) ) ] )
% 1.39/1.83 , clause( 2076, [ 'c_Wellfounded_Owf'(
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 1.39/1.83 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Wellfounded_Owf'(
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 1.39/1.83 , X, Z, Z, Z ), 'c_Relation_Orel__comp'( Y, X, Z, Z, Z ), 'tc_fun'(
% 1.39/1.83 'tc_prod'( Z, Z ), 'tc_bool' ) ), Y, 'tc_fun'( 'tc_prod'( Z, Z ),
% 1.39/1.83 'tc_bool' ) ), Z ) ) ] )
% 1.39/1.83 , clause( 2077, [ =( 'c_Transitive__Closure_Otrancl'( X, Y ),
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_Orel__comp'(
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( X, Y ), X, Y, Y, Y ), 'tc_fun'(
% 1.39/1.83 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ] )
% 1.39/1.83 , clause( 2078, [ =( 'c_Relation_ODomain'( 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.83 X, Y ), Y, Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' )
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 2079, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 1.39/1.83 'tc_prod'( Y, Y ), 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 2080, [ =( 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 1.39/1.83 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2081, [ 'c_Relation_Orefl__on'( 'c_Orderings_Otop__class_Otop'(
% 1.39/1.83 'tc_fun'( X, 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( Y, X ), X )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2082, [ =( 'c_Relation_ORange'( 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.83 X, Y ), Y, Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' )
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 2083, [ 'c_Relation_Oantisym'( 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.83 X, Y ), Y ), ~( 'c_Wellfounded_Oacyclic'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2084, [ 'c_Relation_Osym'(
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_Oconverse'(
% 1.39/1.83 X, Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ] )
% 1.39/1.83 , clause( 2085, [ =( 'c_Relation_ODomain'( 'c_Relation_OId'( X ), X, X ),
% 1.39/1.83 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.39/1.83 , clause( 2086, [ =( 'c_Relation_ORange'( 'c_Relation_OId'( X ), X, X ),
% 1.39/1.83 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.39/1.83 , clause( 2087, [ 'c_Relation_Orefl__on'( 'c_Orderings_Otop__class_Otop'(
% 1.39/1.83 'tc_fun'( X, 'tc_bool' ) ), 'c_Relation_OId'( X ), X ) ] )
% 1.39/1.83 , clause( 2088, [ =( 'c_Relation_OImage'( 'c_Relation_OId__on'( X, Y ), Z,
% 1.39/1.83 Y, Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( Y,
% 1.39/1.83 'tc_bool' ) ) ) ] )
% 1.39/1.83 , clause( 2089, [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'(
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 1.39/1.83 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ) ] )
% 1.39/1.83 , clause( 2090, [ 'c_Relation_Oantisym'(
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 1.39/1.83 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ), ~( 'c_Relation_Oantisym'(
% 1.39/1.83 X, Y ) ) ] )
% 1.39/1.83 , clause( 2091, [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.39/1.83 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), =( Y,
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.83 , clause( 2092, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.39/1.83 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2093, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.39/1.83 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 2094, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.39/1.83 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2095, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1'( T, Z, Y, X ) ), T
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 2096, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_Power_Opower__class_Opower'( T, Y, X ) ),
% 1.39/1.83 'c_Power_Opower__class_Opower'( T, Z, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), T ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2097, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_Power_Opower__class_Opower'( Y, Z, X ) ),
% 1.39/1.83 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), T ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2098, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_Power_Opower__class_Opower'( T, Y, X ) ),
% 1.39/1.83 'c_Power_Opower__class_Opower'( T, Z, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), T ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2099, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_Power_Opower__class_Opower'( Y, Z, X ) ),
% 1.39/1.83 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2100, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Finite__Set_Osetprod'( Y, Z, T, X )
% 1.39/1.83 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( Y,
% 1.39/1.83 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1'( Z, Y, T, X ) ) )
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 2101, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.39/1.83 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ) ), U ), hAPP( hAPP(
% 1.39/1.83 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'( X, X ), Y ), Y, X, X )
% 1.39/1.83 , U ) ), T ) ) ] )
% 1.39/1.83 , clause( 2102, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.39/1.83 Y, X ), Z ), T ) ), U ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ),
% 1.39/1.83 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Z, X,
% 1.39/1.83 'tc_fun'( X, X ), Y ), Y, X, X ), U ) ), T ) ) ] )
% 1.39/1.83 , clause( 2103, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.83 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( Y, Z ),
% 1.39/1.83 'c_Finite__Set_Osetprod'( Y, T, U, X ), X ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 U ), Z ), T ) ) ), ~( 'c_Finite__Set_Ofinite'( T, U ) ) ] )
% 1.39/1.83 , clause( 2104, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.39/1.83 hAPP( 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBS'( 'c_COMBB'(
% 1.39/1.83 'c_HOL_Ominus__class_Ominus'( X ), Z, X, 'tc_fun'( X, X ), Y ), T, Y, X,
% 1.39/1.83 X ) ), U ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.39/1.83 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ), hAPP( hAPP(
% 1.39/1.83 'c_Finite__Set_Osetsum'( Y, X ), T ), U ) ) ) ] )
% 1.39/1.83 , clause( 2105, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBS'( 'c_COMBB'(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( X ), Z, X, 'tc_fun'( X, X ), Y ), T, Y, X, X
% 1.39/1.83 ) ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.39/1.83 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ), hAPP( hAPP(
% 1.39/1.83 'c_Finite__Set_Osetsum'( Y, X ), T ), U ) ) ) ] )
% 1.39/1.83 , clause( 2106, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_in'( T ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1'( Z, Y, T, X ) ), Z
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 2107, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 1.39/1.83 ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), ~( =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.39/1.83 ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ), =( hAPP( Y,
% 1.39/1.83 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1'( Z, Y, T, X
% 1.39/1.83 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.39/1.83 , clause( 2108, [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1'( Y, Z, T, X, U ) ), Y
% 1.39/1.83 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, U ) ), T ),
% 1.39/1.83 'c_Product__Type_OSigma'( Y, Z, X, U ) ) ) ) ] )
% 1.39/1.83 , clause( 2109, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1'( Y, Z, T, X )
% 1.39/1.83 , Z, X, X ) ), T ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 X, X ) ), 'c_Pair'( Y, Z, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T,
% 1.39/1.83 X ) ) ) ) ] )
% 1.39/1.83 , clause( 2110, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1'( Y,
% 1.39/1.83 Z, T, X ), T, X, X ) ), 'c_Transitive__Closure_Ortrancl'( Y, X ) ) ), =(
% 1.39/1.83 Z, T ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, T
% 1.39/1.83 , X, X ) ), 'c_Transitive__Closure_Ortrancl'( Y, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2111, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1'(
% 1.39/1.83 Z, Y, T, X ), X, X ) ), Z ) ), =( Y, T ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2112, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 1.39/1.83 X, Z, T, U ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( U, U ) ), 'c_Pair'( Y, Z, U, U ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( T, U ) ) ) ) ] )
% 1.39/1.83 , clause( 2113, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 1.39/1.83 X, T, U, Z ), T, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ),
% 1.39/1.83 ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z
% 1.39/1.83 ) ), 'c_Pair'( Y, T, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( U, Z )
% 1.39/1.83 ) ) ) ] )
% 1.39/1.83 , clause( 2114, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( Z, Z ) ), 'c_Pair'( T,
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, T,
% 1.39/1.83 U, Z ), Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( X, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ),
% 1.39/1.83 'c_Pair'( T, Y, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( U, Z ) ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2115, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2'( X, Z,
% 1.39/1.83 T, U ) ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( U, U ) ), 'c_Pair'( Z, Y, U, U ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( T, U ) ) ) ) ] )
% 1.39/1.83 , clause( 2116, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, Y, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Y, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~(
% 1.39/1.83 'c_Relation_Osingle__valued'( T, X, X ) ) ] )
% 1.39/1.83 , clause( 2117, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ),
% 1.39/1.83 'c_Pair'( X, 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1'( X, Y, Z )
% 1.39/1.83 , 't_a', 't_a' ) ), 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ) ) ), =(
% 1.39/1.83 Y, X ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ),
% 1.39/1.83 'c_Pair'( X, Y, 't_a', 't_a' ) ), 'c_Transitive__Closure_Ortrancl'( Z,
% 1.39/1.83 't_a' ) ) ) ) ] )
% 1.39/1.83 , clause( 2118, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, Z,
% 1.39/1.83 T, U ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( U, U ) ), 'c_Pair'( Z, Y, U, U ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( T, U ) ) ) ) ] )
% 1.39/1.83 , clause( 2119, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ),
% 1.39/1.83 'c_Pair'( 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1'( X, Y, Z ), Y
% 1.39/1.83 , 't_a', 't_a' ) ), Z ) ), =( Y, X ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( X, Y, 't_a', 't_a' ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ) ) ) ) ] )
% 1.39/1.83 , clause( 2120, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'(
% 1.39/1.83 X, Z, T, U ) ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( U, U ) ), 'c_Pair'( Y, Z, U, U ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( T, U ) ) ) ) ] )
% 1.39/1.83 , clause( 2121, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1'( Y, Z, T, X
% 1.39/1.83 ), X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), =( Y, Z ),
% 1.39/1.83 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.83 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2122, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1'( X, U, T ), T
% 1.39/1.83 , T ) ), U ) ) ), ~( 'c_Wellfounded_Owf'( U, T ) ) ] )
% 1.39/1.83 , clause( 2123, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1'( X, U, T ), T, T ) ), U
% 1.39/1.83 ) ) ), ~( 'c_Wellfounded_Owf'( U, T ) ) ] )
% 1.39/1.83 , clause( 2124, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.39/1.83 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1'( X, U, T ), T, T ) ), U ) )
% 1.39/1.83 ), ~( 'c_Wellfounded_Owf'( U, T ) ) ] )
% 1.39/1.83 , clause( 2125, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1'( X, U, T ), T, T ) )
% 1.39/1.83 , U ) ) ), ~( 'c_Wellfounded_Owf'( U, T ) ) ] )
% 1.39/1.83 , clause( 2126, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.83 'c_Finite__Set_Osetsum'( Z, X ), T, 'tc_fun'( Z, X ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 Z, 'tc_bool' ), X ), Y ), Y, 'tc_fun'( Z, 'tc_bool' ), X ), U ) ), W ),
% 1.39/1.83 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Z, X ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.83 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBC'( T, Y, Z, X ), 'tc_fun'( Y, X
% 1.39/1.83 ), 'tc_fun'( 'tc_fun'( Y, 'tc_bool' ), X ), Z ), Z, 'tc_fun'( Y,
% 1.39/1.83 'tc_bool' ), X ), W ) ), U ) ) ] )
% 1.39/1.83 , clause( 2127, [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.83 'c_Pair'( Y, Y, X, X ) ), Z ) ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 X, X ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1'( Z,
% 1.39/1.83 X ), 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1'(
% 1.39/1.83 Z, X ), X, X ) ), 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ] )
% 1.39/1.83 , clause( 2128, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1'( Y, Z
% 1.39/1.83 , T, X ), T, X, X ) ), 'c_Transitive__Closure_Otrancl'( Y, X ) ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, T, X, X ) ), Y ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, T, X, X
% 1.39/1.83 ) ), 'c_Transitive__Closure_Otrancl'( Y, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2129, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1'( Z, Y, T, X
% 1.39/1.83 ), X, X ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.83 'c_Pair'( Y, T, X, X ) ), 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 2130, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ),
% 1.39/1.83 'c_Pair'( X, 'v_sko__Transitive__Closure__Xtrancl__Xcases__1'( X, Y, Z )
% 1.39/1.83 , 't_a', 't_a' ) ), 'c_Transitive__Closure_Otrancl'( Z, 't_a' ) ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( X, Y,
% 1.39/1.83 't_a', 't_a' ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a',
% 1.39/1.83 't_a' ) ), 'c_Pair'( X, Y, 't_a', 't_a' ) ),
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( Z, 't_a' ) ) ) ) ] )
% 1.39/1.83 , clause( 2131, [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.83 'c_Pair'( Y, Y, X, X ) ), 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ),
% 1.39/1.83 ~( 'c_Wellfounded_Oacyclic'( Z, X ) ) ] )
% 1.39/1.83 , clause( 2132, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1'( Y, Z, T, X ),
% 1.39/1.83 Z, X, X ) ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.83 'c_Pair'( Y, Z, X, X ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 X, X ) ), 'c_Pair'( Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X
% 1.39/1.83 ) ) ) ) ] )
% 1.39/1.83 , clause( 2133, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1'( Y, Z, T, X
% 1.39/1.83 ), X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ), T ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) )
% 1.39/1.83 , 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2134, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1'( Y, Z, T, X )
% 1.39/1.83 , T, X, X ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.83 'c_Pair'( Z, T, X, X ) ), 'c_Transitive__Closure_Otrancl'( Y, X ) ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 2135, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1'( Z
% 1.39/1.83 , Y, T, X ), X, X ) ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X
% 1.39/1.83 ) ), 'c_Pair'( Y, T, X, X ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2136, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ),
% 1.39/1.83 'c_Pair'( 'v_sko__Transitive__Closure__Xtrancl__Xcases__1'( X, Y, Z ), Y
% 1.39/1.83 , 't_a', 't_a' ) ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a',
% 1.39/1.83 't_a' ) ), 'c_Pair'( X, Y, 't_a', 't_a' ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( X, Y, 't_a', 't_a' ) ),
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( Z, 't_a' ) ) ) ) ] )
% 1.39/1.83 , clause( 2137, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X,
% 1.39/1.83 X ), U, Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.39/1.83 'c_Finite__Set_Osetprod'( Y, U, Z, X ) ), 'c_Finite__Set_Osetprod'( T, U
% 1.39/1.83 , Z, X ) ) ) ] )
% 1.39/1.83 , clause( 2138, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1'( Z, T, U, W, V0, Y
% 1.39/1.83 , X ), T, X, Y ) ), W ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( V0, Y
% 1.39/1.83 ) ), 'c_Pair'( Z, T, V0, Y ) ), 'c_Relation_Orel__comp'( U, W, V0, X, Y
% 1.39/1.83 ) ) ) ) ] )
% 1.39/1.83 , clause( 2139, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 Z, 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1'( Z, T, U, W, X,
% 1.39/1.83 V0, Y ), X, Y ) ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, V0
% 1.39/1.83 ) ), 'c_Pair'( Z, T, X, V0 ) ), 'c_Relation_Orel__comp'( U, W, X, Y, V0
% 1.39/1.83 ) ) ) ) ] )
% 1.39/1.83 , clause( 2140, [ =( X, 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Relation__XIdE__1__1'( X, Y ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Relation__XIdE__1__1'( X, Y ), Y, Y ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( Y, Y ) ), X ), 'c_Relation_OId'( Y ) ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2141, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), hAPP( hAPP(
% 1.39/1.83 'c_Finite__Set_Osetsum'( Y, 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.39/1.83 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBB'(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z, 'tc_nat', X, Y ) ), T ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 2142, [ 'c_Wellfounded_Owf'( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 Y ), 'c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1'( X, Y ) ),
% 1.39/1.83 'c_Wellfounded_Oacc'( X, Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2143, [ 'c_Wellfounded_Owf'( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 Y ), 'c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1'( X, Y ) ),
% 1.39/1.83 'c_Wellfounded_Oacc'( X, Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2144, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~(
% 1.39/1.83 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), 'c_Finite__Set_Osetprod'( Y, Z
% 1.39/1.83 , T, 'tc_nat' ) ), 'c_Finite__Set_Osetprod'( 'c_COMBB'(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y, 'tc_nat', X, T ), Z, T, X )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2145, [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, Z, X ) ), Y ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Z ), 'c_Relation_OId__on'(
% 1.39/1.83 Y, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2146, [ =( X, 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, X, Z ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, X, Z ), Z, Z ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), X ), 'c_Relation_OId__on'(
% 1.39/1.83 Y, Z ) ) ) ) ] )
% 1.39/1.83 , clause( 2147, [ =( 'c_Recdef_Ocut'( X, Y, Z, T, U ), 'c_Recdef_Ocut'( W,
% 1.39/1.83 Y, Z, T, U ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'(
% 1.39/1.83 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X, W, Y, Z, T, U ), Z, T, T ) ),
% 1.39/1.83 Y ) ) ] )
% 1.39/1.83 , clause( 2148, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 1.39/1.83 'tc_prod'( Y, Y ), 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 2149, [ =( 'c_Transitive__Closure_Otrancl'(
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 1.39/1.83 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2150, [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 1.39/1.83 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ] )
% 1.39/1.83 , clause( 2151, [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.39/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_OId'( Y ),
% 1.39/1.83 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'( X, Y ), X, Y,
% 1.39/1.83 Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ] )
% 1.39/1.83 , clause( 2152, [ 'c_lessequals'( X, 'c_Relation_Orel__comp'(
% 1.39/1.83 'c_Relation_Oconverse'( X, Y, Y ), X, Y, Y, Y ), 'tc_fun'( 'tc_prod'( Y,
% 1.39/1.83 Y ), 'tc_bool' ) ), ~( 'c_Relation_Orefl__on'( Z, X, Y ) ) ] )
% 1.39/1.83 , clause( 2153, [ =( 'c_Relation_ORange'( 'v_r', 't_a', 't_b' ),
% 1.39/1.83 'c_Relation_ODomain'( 'c_Relation_Oconverse'( 'v_r', 't_a', 't_b' ),
% 1.39/1.83 't_b', 't_a' ) ) ] )
% 1.39/1.83 , clause( 2154, [ 'c_Relation_Oirrefl'( X, Y ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( Y, Y ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1'( X, Y ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1'( X, Y ), Y, Y ) ), X )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2155, [ 'c_Equiv__Relations_Ocongruent'( X, hAPP( Y, Z ), T, U )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_in'( W ), Z ), V0 ) ) ), ~(
% 1.39/1.83 'c_Equiv__Relations_Ocongruent2'( V1, X, Y, W, T, U ) ), ~(
% 1.39/1.83 'c_Equiv__Relations_Oequiv'( V0, V1, W ) ) ] )
% 1.39/1.83 , clause( 2156, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Wellfounded_Omlex__prod'( T, U, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ), U ) )
% 1.39/1.83 ), ~( 'c_lessequals'( hAPP( T, Y ), hAPP( T, Z ), 'tc_nat' ) ) ] )
% 1.39/1.83 , clause( 2157, [ 'c_Nitpick_Orefl_H'( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( Y, Y ) ), 'c_Pair'(
% 1.39/1.83 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1'( X, Y ),
% 1.39/1.83 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1'( X, Y ), Y, Y ) ), X ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2158, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_Power_Opower__class_Opower'( Y, Z, X ) ),
% 1.39/1.83 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( 'tc_nat' ), T ), Z ) ) ) ] )
% 1.39/1.83 , clause( 2159, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Finite__Set_Osetprod'( Y, Z, T, X )
% 1.39/1.83 ) ), hBOOL( hAPP( hAPP( 'c_in'( T ),
% 1.39/1.83 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1'( Z, Y, T, X ) ), Z
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 2160, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2161, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 'tc_nat' ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2162, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 1.39/1.83 ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), ~( =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.39/1.83 ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ), hBOOL( hAPP( hAPP( 'c_in'( T )
% 1.39/1.83 , 'c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1'( Z, Y, T,
% 1.39/1.83 X ) ), Z ) ) ] )
% 1.39/1.83 , clause( 2163, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1'( Z, T, X ), X, X ) ),
% 1.39/1.83 T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), U ), Z ) ) ), ~(
% 1.39/1.83 'c_Wellfounded_Owf'( T, X ) ) ] )
% 1.39/1.83 , clause( 2164, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y,
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1'( Z, T, X ), X,
% 1.39/1.83 X ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), U ), Z ) ) ), ~(
% 1.39/1.83 'c_Wellfounded_Owf'( T, X ) ) ] )
% 1.39/1.83 , clause( 2165, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Relation__XImageE__1__1'( Z, T, U, X, Y ), T, X, Y )
% 1.39/1.83 ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), T ), 'c_Relation_OImage'( U
% 1.39/1.83 , Z, X, Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2166, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1'( Z, T, U, X, Y ), T, X
% 1.39/1.83 , Y ) ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), T ),
% 1.39/1.83 'c_Relation_OImage'( U, Z, X, Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2167, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.39/1.83 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.83 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z,
% 1.39/1.83 X, X ), U, Z, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ),
% 1.39/1.83 'c_Finite__Set_Osetprod'( Y, U, Z, X ) ), 'c_Finite__Set_Osetprod'( T, U
% 1.39/1.83 , Z, X ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ) ] )
% 1.39/1.83 , clause( 2168, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 Z, 'c_ATP__Linkup_Osko__Relation__XDomainE__1__1'( Z, T, X, Y ), X, Y ) )
% 1.39/1.83 , T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), 'c_Relation_ODomain'( T
% 1.39/1.83 , X, Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2169, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 Z, 'c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1'( Z, T, X, Y ), X, Y
% 1.39/1.83 ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), 'c_Relation_ODomain'(
% 1.39/1.83 T, X, Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2170, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1'( Y, Z, X ), Z, X
% 1.39/1.83 , X ) ), Y ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), 'c_Wellfounded_Oacc'(
% 1.39/1.83 Y, X ) ) ) ] )
% 1.39/1.83 , clause( 2171, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, U, T ), T
% 1.39/1.83 , T ) ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ),
% 1.39/1.83 'c_Wellfounded_Oacc'( U, T ) ) ) ) ] )
% 1.39/1.83 , clause( 2172, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( Z,
% 1.39/1.83 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, T ), 't_a', 't_a' ) ), T ) ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( T,
% 1.39/1.83 't_a' ) ) ) ) ] )
% 1.39/1.83 , clause( 2173, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'(
% 1.39/1.83 Z, X ) ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1'( Z, Y, X ), Y, X,
% 1.39/1.83 X ) ), Z ) ) ] )
% 1.39/1.83 , clause( 2174, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( 't_a' )
% 1.39/1.83 , Z ), 'c_Wellfounded_Oacc'( T, 't_a' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( Z,
% 1.39/1.83 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, T ), 't_a', 't_a' ) ), T ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( T,
% 1.39/1.83 't_a' ) ) ) ) ] )
% 1.39/1.83 , clause( 2175, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( Z,
% 1.39/1.83 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, T ), 't_a', 't_a' ) ), T ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( T,
% 1.39/1.83 't_a' ) ) ) ) ] )
% 1.39/1.83 , clause( 2176, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_in'( 't_a' )
% 1.39/1.83 , Z ), 'c_Wellfounded_Oacc'( T, 't_a' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( 't_a', 't_a' ) ), 'c_Pair'( Z,
% 1.39/1.83 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, T ), 't_a', 't_a' ) ), T ) ) )
% 1.39/1.83 , ~( hBOOL( hAPP( hAPP( 'c_in'( 't_a' ), Y ), 'c_Wellfounded_Oacc'( T,
% 1.39/1.83 't_a' ) ) ) ) ] )
% 1.39/1.83 , clause( 2177, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Z,
% 1.39/1.83 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, U, T ), T, T )
% 1.39/1.83 ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), 'c_Wellfounded_Oacc'(
% 1.39/1.83 U, T ) ) ) ) ] )
% 1.39/1.83 , clause( 2178, [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.83 'c_Pair'( Y, Z, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) )
% 1.39/1.83 , ~( 'c_Wellfounded_Owf'( 'c_Set_Oinsert'( 'c_Pair'( Z, Y, X, X ), T,
% 1.39/1.83 'tc_prod'( X, X ) ), X ) ) ] )
% 1.39/1.83 , clause( 2179, [ 'c_Wellfounded_Owf'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z,
% 1.39/1.83 Z ), T, 'tc_prod'( Z, Z ) ), Z ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z
% 1.39/1.83 , Z ) ), 'c_Pair'( Y, X, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( T, Z
% 1.39/1.83 ) ) ), ~( 'c_Wellfounded_Owf'( T, Z ) ) ] )
% 1.39/1.83 , clause( 2180, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Relation__XRangeE__1__1'( Z, T, Y, X ), Z, X, Y ) )
% 1.39/1.83 , T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), 'c_Relation_ORange'( T,
% 1.39/1.83 X, Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2181, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Relation__XRange__iff__1__1'( Z, T, Y, X ), Z, X, Y
% 1.39/1.83 ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), 'c_Relation_ORange'(
% 1.39/1.83 T, X, Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2182, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1'( Z, Y, T, X
% 1.39/1.83 ), X, X ) ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( Z, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2183, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1'( Y, Z, T, X ),
% 1.39/1.83 T, X, X ) ), 'c_Transitive__Closure_Ortrancl'( Y, X ) ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, T, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( Y, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2184, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.83 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y, 'tc_bool' ), Z
% 1.39/1.83 ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X
% 1.39/1.83 , X ) ), Y, X, X ), U ), W, Y, X ), 'c_Power_Opower__class_Opower'( U,
% 1.39/1.83 'c_Finite__Set_Ocard'( W, Y ), X ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z )
% 1.39/1.83 , W ) ), ~( 'c_Finite__Set_Ofinite'( W, Y ) ) ] )
% 1.39/1.83 , clause( 2185, [ =( 'c_Set_Ovimage'( hAPP( 'c_COMBC'( hAPP( 'c_COMBC'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y
% 1.39/1.83 , 'tc_bool' ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X )
% 1.39/1.83 ), Y ), Y, X, 'tc_fun'( X, X ) ), T ), Y, X, X ), U ), W, Y, X ), hAPP(
% 1.39/1.83 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), Z ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_in'( X ), U ), W ) ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 X ), T ), W ) ) ] )
% 1.39/1.83 , clause( 2186, [ =( 'c_Set_Ovimage'( hAPP( 'c_COMBC'( hAPP( 'c_COMBC'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y
% 1.39/1.83 , 'tc_bool' ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X )
% 1.39/1.83 ), Y ), Y, X, 'tc_fun'( X, X ) ), T ), Y, X, X ), U ), W, Y, X ),
% 1.39/1.83 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( X ), U ), W ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X )
% 1.39/1.83 , T ), W ) ) ) ] )
% 1.39/1.83 , clause( 2187, [ =( 'c_Set_Ovimage'( hAPP( 'c_COMBC'( hAPP( 'c_COMBC'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y
% 1.39/1.83 , 'tc_bool' ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X )
% 1.39/1.83 ), Y ), Y, X, 'tc_fun'( X, X ) ), T ), Y, X, X ), U ), W, Y, X ),
% 1.39/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( X ), U ), W ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), T ), W ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2188, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ),
% 1.39/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( T, U, 'tc_fun'( Y,
% 1.39/1.83 'tc_bool' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP(
% 1.39/1.83 'c_COMBC'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'(
% 1.39/1.83 'c_in'( Y ), Y, 'tc_fun'( Y, 'tc_bool' ), 'tc_bool' ), U ), 'tc_bool',
% 1.39/1.83 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), Z, Y, X, 'tc_fun'( X, X ) ), Y, X,
% 1.39/1.83 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), T ) ), ~(
% 1.39/1.83 'c_Finite__Set_Ofinite'( T, Y ) ) ] )
% 1.39/1.83 , clause( 2189, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 Z, T, X, Y ) ), 'c_Relation_Oconverse'( U, Y, X ) ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( 'tc_prod'( Y, X ) ), 'c_Pair'( T, Z, Y, X ) ), U ) ) ) ] )
% 1.39/1.83 , clause( 2190, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 Z, T, X, Y ) ), 'c_Relation_Oconverse'( U, Y, X ) ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( 'tc_prod'( Y, X ) ), 'c_Pair'( T, Z, Y, X ) ), U ) ) ) ] )
% 1.39/1.83 , clause( 2191, [ =( hAPP( 'c_Recdef_Ocut'( X, Y, Z, T, U ), W ), hAPP( X,
% 1.39/1.83 W ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( W, Z
% 1.39/1.83 , T, T ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2192, [ =( hAPP( 'c_Recdef_Ocut'( X, Y, Z, T, U ), W ), hAPP( X,
% 1.39/1.83 W ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( W, Z
% 1.39/1.83 , T, T ) ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2193, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.83 'c_HOL_OIf'( X ), hAPP( 'c_fequal'( Y ), Z ), 'tc_bool', 'tc_fun'( X,
% 1.39/1.83 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X ) ), Y, X, X ),
% 1.39/1.83 'c_HOL_Oone__class_Oone'( X ) ), U, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.39/1.83 ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U ) ), ~(
% 1.39/1.83 'c_Finite__Set_Ofinite'( U, Y ) ) ] )
% 1.39/1.83 , clause( 2194, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBS'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_OIf'( X ), hAPP( 'c_fequal'( Y ), Z ), 'tc_bool',
% 1.39/1.83 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X ) ), Y, X,
% 1.39/1.83 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), U ), hAPP( T, Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( Y ), Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Y )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2195, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBS'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_OIf'( X ), hAPP( 'c_fequal'( Y ), Z ), 'tc_bool',
% 1.39/1.83 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X ) ), Y, X,
% 1.39/1.83 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), U ), 'c_HOL_Ozero__class_Ozero'(
% 1.39/1.83 X ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U ) ), ~(
% 1.39/1.83 'c_Finite__Set_Ofinite'( U, Y ) ) ] )
% 1.39/1.83 , clause( 2196, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.83 'c_HOL_OIf'( X ), hAPP( 'c_fequal'( Y ), Z ), 'tc_bool', 'tc_fun'( X,
% 1.39/1.83 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X ) ), Y, X, X ),
% 1.39/1.83 'c_HOL_Oone__class_Oone'( X ) ), U, Y, X ), hAPP( T, Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( Y ), Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Y )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2197, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z
% 1.39/1.83 ) ), 'c_Pair'( X, Y, Z, Z ) ), 'c_Transitive__Closure_Ortrancl'( T, Z )
% 1.39/1.83 ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), 'c_Relation_ODomain'( T, Z,
% 1.39/1.83 Z ) ) ) ] )
% 1.39/1.83 , clause( 2198, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ODomain'(
% 1.39/1.83 Z, X, X ) ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Y, X, X ) ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ] )
% 1.39/1.83 , clause( 2199, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'(
% 1.39/1.83 Z, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, T, X, X ) ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( X ), T ), 'c_Wellfounded_Oacc'( Z, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2200, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'(
% 1.39/1.83 Z, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), 'c_Wellfounded_Oacc'(
% 1.39/1.83 Z, X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, T, X, X ) ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2201, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( X, X ) ), Y ), Z ) ) ) ] )
% 1.39/1.83 , clause( 2202, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), Y ),
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( X, X ) ), Y ), Z ) ) ) ] )
% 1.39/1.83 , clause( 2203, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ), T ) ) ) ] )
% 1.39/1.83 , clause( 2204, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ), T ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X
% 1.39/1.83 , X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2205, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ), =( Y, Z ) ] )
% 1.39/1.83 , clause( 2206, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), =( Y, Z ),
% 1.39/1.83 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.83 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2207, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), =( Y, Z ),
% 1.39/1.83 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.39/1.83 ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2208, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Ortrancl'( 'c_Relation_Oconverse'(
% 1.39/1.83 T, X, X ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.83 'c_Pair'( Z, Y, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2209, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, Y, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( 'c_Relation_Oconverse'( T, X, X ), X )
% 1.39/1.83 ) ) ) ] )
% 1.39/1.83 , clause( 2210, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2211, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2212, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2213, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Relation_Oconverse'( 'c_Transitive__Closure_Otrancl'(
% 1.39/1.83 T, X ), X, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.83 'c_Pair'( Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'(
% 1.39/1.83 'c_Relation_Oconverse'( T, X, X ), X ) ) ) ) ] )
% 1.39/1.83 , clause( 2214, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( 'c_Relation_Oconverse'(
% 1.39/1.83 T, X, X ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.83 'c_Pair'( Y, Z, X, X ) ), 'c_Relation_Oconverse'(
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( T, X ), X, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2215, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ),
% 1.39/1.83 ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2216, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ),
% 1.39/1.83 ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2217, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 1.39/1.83 T, X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2218, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 1.39/1.83 T, X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2219, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 1.39/1.83 T, X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2220, [ ~( =( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X,
% 1.39/1.83 'tc_bool' ), 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'(
% 1.39/1.83 X, 'tc_bool' ), 'tc_bool' ), Z ) ) ), =( Y, Z ) ] )
% 1.39/1.83 , clause( 2221, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'(
% 1.39/1.83 Z, X ) ) ), ~( 'c_Wellfounded_Owf'( Z, X ) ) ] )
% 1.39/1.83 , clause( 2222, [ 'c_Relation_Osym'( 'c_Transitive__Closure_Otrancl'( X, Y
% 1.39/1.83 ), Y ), ~( 'c_Relation_Osym'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2223, [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ),
% 1.39/1.83 'c_Finite__Set_Ofinite'( Y, X ) ] )
% 1.39/1.83 , clause( 2224, [ 'c_Relation_Osym'( X, Y ), ~( 'c_Relation_Osym'(
% 1.39/1.83 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ] )
% 1.39/1.83 , clause( 2225, [ 'c_Relation_Osym'( 'c_Relation_Oconverse'( X, Y, Y ), Y )
% 1.39/1.83 , ~( 'c_Relation_Osym'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2226, [ =( 'c_Relation_ODomain'( 'c_Transitive__Closure_Otrancl'(
% 1.39/1.83 X, Y ), Y, Y ), 'c_Relation_ODomain'( X, Y, Y ) ) ] )
% 1.39/1.83 , clause( 2227, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.39/1.83 ~( =( hAPP( Y, Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( T ), Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ),
% 1.39/1.83 =( 'c_Finite__Set_Osetprod'( Y, U, T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.39/1.83 ) ) ] )
% 1.39/1.83 , clause( 2228, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 1.39/1.83 ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), ~( =( hAPP( Y, Z )
% 1.39/1.83 , 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T )
% 1.39/1.83 , Z ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ), =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( Y, U, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2229, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ] )
% 1.39/1.83 , clause( 2230, [ 'c_Relation_Osym'( 'c_Relation_OId'( X ), X ) ] )
% 1.39/1.83 , clause( 2231, [ =( 'c_Relation_Orel__comp'( 'c_Relation_OId'( X ), Y, X,
% 1.39/1.83 X, Z ), Y ) ] )
% 1.39/1.83 , clause( 2232, [ =( 'c_Relation_Orel__comp'( X, 'c_Relation_OId'( Y ), Z,
% 1.39/1.83 Y, Y ), X ) ] )
% 1.39/1.83 , clause( 2233, [ 'c_Relation_Oantisym'( 'c_Relation_OId__on'( X, Y ), Y )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2234, [ 'c_Wellfounded_Owf'( 'c_Relation_Oconverse'(
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y ), Y ), ~(
% 1.39/1.83 'c_Wellfounded_Owf'( 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ] )
% 1.39/1.83 , clause( 2235, [ 'c_Relation_Orefl__on'( X, Y, Z ), ~(
% 1.39/1.83 'c_Relation_Orefl__on'( X, 'c_Relation_Oconverse'( Y, Z, Z ), Z ) ) ] )
% 1.39/1.83 , clause( 2236, [ 'c_Relation_Orefl__on'( X, 'c_Relation_Oconverse'( Y, Z,
% 1.39/1.83 Z ), Z ), ~( 'c_Relation_Orefl__on'( X, Y, Z ) ) ] )
% 1.39/1.83 , clause( 2237, [ 'c_Relation_Osym'( 'c_Transitive__Closure_Ortrancl'( X, Y
% 1.39/1.83 ), Y ), ~( 'c_Relation_Osym'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2238, [ 'c_Wellfounded_Owf'( 'c_Relation_Orel__comp'( X, X, Y, Y
% 1.39/1.83 , Y ), Y ), ~( 'c_Wellfounded_Owf'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2239, [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_Wellfounded_Owf'(
% 1.39/1.83 'c_Relation_Orel__comp'( X, X, Y, Y, Y ), Y ) ) ] )
% 1.39/1.83 , clause( 2240, [ =( 'c_Relation_OImage'( 'c_Relation_OId'( X ), Y, X, X )
% 1.39/1.83 , Y ) ] )
% 1.39/1.83 , clause( 2241, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.39/1.83 =( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 2242, [ =( 'c_Relation_ODomain'( 'c_Relation_OId__on'( X, Y ), Y
% 1.39/1.83 , Y ), X ) ] )
% 1.39/1.83 , clause( 2243, [ =( 'c_Relation_Oconverse'( X, Y, Y ), X ), ~(
% 1.39/1.83 'c_Relation_Osym'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2244, [ ~( =( 'c_Relation_Oconverse'( X, Y, Y ), X ) ),
% 1.39/1.83 'c_Relation_Osym'( X, Y ) ] )
% 1.39/1.83 , clause( 2245, [ =( 'c_Relation_ORange'( 'c_Transitive__Closure_Otrancl'(
% 1.39/1.83 X, Y ), Y, Y ), 'c_Relation_ORange'( X, Y, Y ) ) ] )
% 1.39/1.83 , clause( 2246, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.39/1.83 'c_Finite__Set_Ofinite'( Z, T ) ] )
% 1.39/1.83 , clause( 2247, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( Y, Z, T, X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.39/1.83 'c_Finite__Set_Ofinite'( Z, T ) ] )
% 1.39/1.83 , clause( 2248, [ =( 'c_Relation_Oconverse'( 'c_Relation_Orel__comp'( X, Y
% 1.39/1.83 , Z, T, U ), Z, U ), 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( Y,
% 1.39/1.83 T, U ), 'c_Relation_Oconverse'( X, Z, T ), U, T, Z ) ) ] )
% 1.39/1.83 , clause( 2249, [ 'c_Relation_Osym'( 'c_Relation_OId__on'( X, Y ), Y ) ] )
% 1.39/1.83 , clause( 2250, [ 'c_Relation_Orefl__on'( X, 'c_Relation_OId__on'( X, Y ),
% 1.39/1.83 Y ) ] )
% 1.39/1.83 , clause( 2251, [ 'c_Wellfounded_Owf'( 'c_Relation_Oinv__image'( X, Y, Z, T
% 1.39/1.83 ), T ), ~( 'c_Wellfounded_Owf'( X, Z ) ) ] )
% 1.39/1.83 , clause( 2252, [ =( 'c_Relation_Orel__comp'( X,
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y, Y ),
% 1.39/1.83 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'( X, Y ), X, Y,
% 1.39/1.83 Y, Y ) ) ] )
% 1.39/1.83 , clause( 2253, [ 'c_Relation_Osym'( 'c_Relation_Oinv__image'( X, Y, Z, T )
% 1.39/1.83 , T ), ~( 'c_Relation_Osym'( X, Z ) ) ] )
% 1.39/1.83 , clause( 2254, [ =( 'c_Transitive__Closure_Otrancl'(
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( X, Y ), Y ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2255, [ =( 'c_Relation_Oconverse'( 'c_Relation_OId'( X ), X, X )
% 1.39/1.83 , 'c_Relation_OId'( X ) ) ] )
% 1.39/1.83 , clause( 2256, [ 'c_Wellfounded_Owf'( 'c_Transitive__Closure_Otrancl'( X,
% 1.39/1.83 Y ), Y ), ~( 'c_Wellfounded_Owf'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2257, [ =( 'c_Relation_Orel__comp'( 'c_Relation_Orel__comp'( X, Y
% 1.39/1.83 , Z, T, U ), W, Z, U, V0 ), 'c_Relation_Orel__comp'( X,
% 1.39/1.83 'c_Relation_Orel__comp'( Y, W, T, U, V0 ), Z, T, V0 ) ) ] )
% 1.39/1.83 , clause( 2258, [ =( 'c_Relation_Oconverse'( 'c_Relation_Oinv__image'( X, Y
% 1.39/1.83 , Z, T ), T, T ), 'c_Relation_Oinv__image'( 'c_Relation_Oconverse'( X, Z
% 1.39/1.83 , Z ), Y, Z, T ) ) ] )
% 1.39/1.83 , clause( 2259, [ =( 'c_Transitive__Closure_Otrancl'(
% 1.39/1.83 'c_Relation_Oconverse'( X, Y, Y ), Y ), 'c_Relation_Oconverse'(
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y ) ) ] )
% 1.39/1.83 , clause( 2260, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =( hAPP(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), hAPP(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ) ), =( Y, Z ) ] )
% 1.39/1.83 , clause( 2261, [ =( 'c_Relation_Oconverse'( 'c_Relation_OId__on'( X, Y ),
% 1.39/1.83 Y, Y ), 'c_Relation_OId__on'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2262, [ ~( =( 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X
% 1.39/1.83 , Y, Y ), X, Y, Y, Y ), X ) ), 'c_Equiv__Relations_Oequiv'(
% 1.39/1.83 'c_Relation_ODomain'( X, Y, Y ), X, Y ) ] )
% 1.39/1.83 , clause( 2263, [ 'c_Relation_Oantisym'( 'c_Relation_OId'( X ), X ) ] )
% 1.39/1.83 , clause( 2264, [ 'c_Wellfounded_Owf'( 'c_Wellfounded_Omlex__prod'( X, Y, Z
% 1.39/1.83 ), Z ), ~( 'c_Wellfounded_Owf'( Y, Z ) ) ] )
% 1.39/1.83 , clause( 2265, [ =( 'c_Relation_ORange'( 'c_Relation_Oconverse'( X, Y, Z )
% 1.39/1.83 , Z, Y ), 'c_Relation_ODomain'( X, Y, Z ) ) ] )
% 1.39/1.83 , clause( 2266, [ =( 'c_Relation_ORange'( 'c_Relation_OId__on'( X, Y ), Y,
% 1.39/1.83 Y ), X ) ] )
% 1.39/1.83 , clause( 2267, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 2268, [ =( 'c_Relation_Oconverse'( 'c_Relation_Oconverse'( X, Y,
% 1.39/1.83 Z ), Z, Y ), X ) ] )
% 1.39/1.83 , clause( 2269, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.39/1.83 =( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 2270, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Finite__Set_Ofinite'( T, Y ) ] )
% 1.39/1.83 , clause( 2271, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Finite__Set_Ofinite'( T, Y ) ] )
% 1.39/1.83 , clause( 2272, [ =( 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X, Y
% 1.39/1.83 , Y ), X, Y, Y, Y ), X ), ~( 'c_Equiv__Relations_Oequiv'( Z, X, Y ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 2273, [ =( 'c_Relation_Orel__comp'(
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y, Y ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2274, [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'(
% 1.39/1.83 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ] )
% 1.39/1.83 , clause( 2275, [ 'c_Relation_Oantisym'( 'c_Relation_Oconverse'( X, Y, Y )
% 1.39/1.83 , Y ), ~( 'c_Relation_Oantisym'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2276, [ 'c_Relation_Orefl__on'( X, Y, Z ), ~(
% 1.39/1.83 'c_Equiv__Relations_Oequiv'( X, Y, Z ) ) ] )
% 1.39/1.83 , clause( 2277, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.39/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ) ] )
% 1.39/1.83 , clause( 2278, [ =( 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.83 'c_Relation_Oconverse'( X, Y, Y ), Y ), 'c_Relation_Oconverse'(
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y ) ) ] )
% 1.39/1.83 , clause( 2279, [ 'c_Relation_Osym'( X, Y ), ~( 'c_Equiv__Relations_Oequiv'(
% 1.39/1.83 Z, X, Y ) ) ] )
% 1.39/1.83 , clause( 2280, [ =( 'c_Relation_ODomain'( 'c_Relation_Oconverse'( X, Y, Z
% 1.39/1.83 ), Z, Y ), 'c_Relation_ORange'( X, Y, Z ) ) ] )
% 1.39/1.83 , clause( 2281, [ =( 'c_Transitive__Closure_Otrancl'( X, Y ),
% 1.39/1.83 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'( X, Y ), X, Y,
% 1.39/1.83 Y, Y ) ) ] )
% 1.39/1.83 , clause( 2282, [ =( 'c_Transitive__Closure_Otrancl'( X, Y ),
% 1.39/1.83 'c_Relation_Orel__comp'( X, 'c_Transitive__Closure_Ortrancl'( X, Y ), Y,
% 1.39/1.83 Y, Y ) ) ] )
% 1.39/1.83 , clause( 2283, [ =( 'c_Relation_ORange'( X, Y, Z ), 'c_Relation_ODomain'(
% 1.39/1.83 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ) ) ] )
% 1.39/1.83 , clause( 2284, [ 'c_Relation_Ototal__on'( X, Y, Z ), ~(
% 1.39/1.83 'c_Relation_Ototal__on'( X, 'c_Relation_Oconverse'( Y, Z, Z ), Z ) ) ] )
% 1.39/1.83 , clause( 2285, [ 'c_Relation_Ototal__on'( X, 'c_Relation_Oconverse'( Y, Z
% 1.39/1.83 , Z ), Z ), ~( 'c_Relation_Ototal__on'( X, Y, Z ) ) ] )
% 1.39/1.83 , clause( 2286, [ hBOOL( hAPP( X, hAPP( Y, Z ) ) ), ~( hBOOL( hAPP(
% 1.39/1.83 'c_Set_Ovimage'( Y, X, T, U ), Z ) ) ) ] )
% 1.39/1.83 , clause( 2287, [ hBOOL( hAPP( 'c_Set_Ovimage'( X, Y, Z, T ), U ) ), ~(
% 1.39/1.83 hBOOL( hAPP( Y, hAPP( X, U ) ) ) ) ] )
% 1.39/1.83 , clause( 2288, [ 'c_Wellfounded_Owf'( 'c_Wellfounded_Omeasure'( X, Y ), Y
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2289, [ =( 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( X, Y ), Y ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2290, [ =( 'c_Transitive__Closure_Ortrancl'(
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( X, Y ), Y ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ] )
% 1.39/1.83 , clause( 2291, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 Z, T, X, Y ) ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Y, X ) )
% 1.39/1.83 , 'c_Pair'( T, Z, Y, X ) ), 'c_Relation_Oconverse'( U, X, Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2292, [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.83 'c_Pair'( Y, Y, X, X ) ), Z ) ) ), ~( 'c_Relation_Oirrefl'( Z, X ) ) ] )
% 1.39/1.83 , clause( 2293, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ), T ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X
% 1.39/1.83 , X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2294, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ), T ) ) ) ] )
% 1.39/1.83 , clause( 2295, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ), T ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X
% 1.39/1.83 , X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2296, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ), T ) ) ) ] )
% 1.39/1.83 , clause( 2297, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X ) ), T ) )
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2298, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Ortrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Ortrancl'( T, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2299, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Y, X, X ) ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ] )
% 1.39/1.83 , clause( 2300, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Y, X, X ) ), 'c_Transitive__Closure_Ortrancl'( Z, X ) ) ) ] )
% 1.39/1.83 , clause( 2301, [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.83 'c_Pair'( Y, Z, X, X ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( X, X ) ), 'c_Pair'( Z, Y, X, X ) ), T ) ) ), ~(
% 1.39/1.83 'c_Wellfounded_Owf'( T, X ) ) ] )
% 1.39/1.83 , clause( 2302, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z
% 1.39/1.83 ) ), 'c_Pair'( Y, X, Z, Z ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( Z, Z ) ), 'c_Pair'( X, Y, Z, Z ) ), T ) ) ), ~(
% 1.39/1.83 'c_Relation_Oantisym'( T, Z ) ) ] )
% 1.39/1.83 , clause( 2303, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z
% 1.39/1.83 ) ), 'c_Pair'( Y, X, Z, Z ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( Z, Z ) ), 'c_Pair'( X, Y, Z, Z ) ), T ) ) ), ~(
% 1.39/1.83 'c_Relation_Oantisym'( T, Z ) ) ] )
% 1.39/1.83 , clause( 2304, [ =( hAPP( X, Y ), hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( Y, Z, T, T ) ), U ) ) ), ~(
% 1.39/1.83 'c_Equiv__Relations_Ocongruent'( U, X, T, W ) ) ] )
% 1.39/1.83 , clause( 2305, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z
% 1.39/1.83 ) ), 'c_Pair'( X, Y, Z, Z ) ), 'c_Relation_OId__on'( T, Z ) ) ) ) ] )
% 1.39/1.83 , clause( 2306, [ ~( =( 'c_Recdef_Ocut'( X, Y, Z, T, U ), 'c_Recdef_Ocut'(
% 1.39/1.83 W, Y, Z, T, U ) ) ), =( hAPP( X, V0 ), hAPP( W, V0 ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( 'tc_prod'( T, T ) ), 'c_Pair'( V0, Z, T, T ) ), Y ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 2307, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z
% 1.39/1.83 ) ), 'c_Pair'( X, Y, Z, Z ) ), 'c_Relation_OId'( Z ) ) ) ) ] )
% 1.39/1.83 , clause( 2308, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Y, X, X ) ), Z ) ), ~( 'c_Nitpick_Orefl_H'( Z, X ) ) ] )
% 1.39/1.83 , clause( 2309, [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.83 'c_Pair'( Y, Y, X, X ) ), Z ) ) ), ~( 'c_Wellfounded_Owf'( Z, X ) ) ] )
% 1.39/1.83 , clause( 2310, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Relation_Oinv__image'( T, U, W, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( W, W ) ), 'c_Pair'( hAPP( U, Y ), hAPP( U
% 1.39/1.83 , Z ), W, W ) ), T ) ) ) ] )
% 1.39/1.83 , clause( 2311, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 hAPP( Y, Z ), hAPP( Y, T ), X, X ) ), U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( W, W ) ), 'c_Pair'( Z, T, W, W ) ), 'c_Relation_Oinv__image'(
% 1.39/1.83 U, Y, X, W ) ) ) ) ] )
% 1.39/1.83 , clause( 2312, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) )
% 1.39/1.83 , 'c_Pair'( Z, Y, X, X ) ), T ) ) ), ~( 'c_Relation_Osym'( T, X ) ) ] )
% 1.39/1.83 , clause( 2313, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) )
% 1.39/1.83 , 'c_Pair'( Z, Y, X, X ) ), T ) ) ), ~( 'c_Relation_Osym'( T, X ) ) ] )
% 1.39/1.83 , clause( 2314, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 Z, T, X, Y ) ), 'c_Relation_Orel__comp'( U, W, X, V0, Y ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( V0, Y ) ), 'c_Pair'( V1, T, V0, Y ) ), W )
% 1.39/1.83 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, V0 ) ), 'c_Pair'( Z, V1
% 1.39/1.83 , X, V0 ) ), U ) ) ) ] )
% 1.39/1.83 , clause( 2315, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ), T ) )
% 1.39/1.83 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X
% 1.39/1.83 , X ) ), T ) ) ) ] )
% 1.39/1.83 , clause( 2316, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Transitive__Closure_Otrancl'( T, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( U, Z, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, U, X, X ) ),
% 1.39/1.83 'c_Transitive__Closure_Otrancl'( T, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2317, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Y, X, X ) ), 'c_Relation_OId'( X ) ) ) ] )
% 1.39/1.83 , clause( 2318, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Y, X, X ) ), 'c_Relation_OId'( X ) ) ) ] )
% 1.39/1.83 , clause( 2319, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), ~(
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ), hAPP(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ) ) ) ] )
% 1.39/1.83 , clause( 2320, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ), hAPP(
% 1.39/1.83 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ) ] )
% 1.39/1.83 , clause( 2321, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ),
% 1.39/1.83 'v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1'( X, Y ) ) ), =( X, Y
% 1.39/1.83 ) ] )
% 1.39/1.83 , clause( 2322, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.83 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y, 'tc_bool' ), Z
% 1.39/1.83 ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X
% 1.39/1.83 , X ) ), Y, X, X ), 'c_HOL_Oone__class_Oone'( X ) ), U, Y, X ),
% 1.39/1.83 'c_HOL_Oone__class_Oone'( X ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U )
% 1.39/1.83 ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ] )
% 1.39/1.83 , clause( 2323, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBS'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y,
% 1.39/1.83 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y,
% 1.39/1.83 X, 'tc_fun'( X, X ) ), Y, X, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), U
% 1.39/1.83 ), hAPP( T, Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U ) ) ), ~(
% 1.39/1.83 'c_Finite__Set_Ofinite'( U, Y ) ) ] )
% 1.39/1.83 , clause( 2324, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.39/1.83 'c_Finite__Set_Osetprod'( hAPP( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'(
% 1.39/1.83 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y, 'tc_bool' ), Z
% 1.39/1.83 ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X
% 1.39/1.83 , X ) ), Y, X, X ), 'c_HOL_Oone__class_Oone'( X ) ), U, Y, X ), hAPP( T,
% 1.39/1.83 Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U ) ) ), ~(
% 1.39/1.83 'c_Finite__Set_Ofinite'( U, Y ) ) ] )
% 1.39/1.83 , clause( 2325, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.39/1.83 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBS'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_fequal'( Y ), Y, Y,
% 1.39/1.83 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y,
% 1.39/1.83 X, 'tc_fun'( X, X ) ), Y, X, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), U
% 1.39/1.83 ), 'c_HOL_Ozero__class_Ozero'( X ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z
% 1.39/1.83 ), U ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ] )
% 1.39/1.83 , clause( 2326, [ =( 'c_Set_Ovimage'( hAPP( 'c_COMBC'( hAPP( 'c_COMBC'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_OIf'( X ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y
% 1.39/1.83 , 'tc_bool' ), 'tc_bool' ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X )
% 1.39/1.83 ), Y ), Y, X, 'tc_fun'( X, X ) ), T ), Y, X, X ), U ), W, Y, X ), Z ),
% 1.39/1.83 hBOOL( hAPP( hAPP( 'c_in'( X ), U ), W ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 X ), T ), W ) ) ) ] )
% 1.39/1.83 , clause( 2327, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 Z, T, X, Y ) ), 'c_Product__Type_OSigma'( U, W, X, Y ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( Y ), T ), hAPP( W, Z ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( X ), Z ), U ) ) ) ] )
% 1.39/1.83 , clause( 2328, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'(
% 1.39/1.83 Z, T, X, Y ) ), 'c_Product__Type_OSigma'( U, W, X, Y ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( Y ), T ), hAPP( W, Z ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( X ), Z ), U ) ) ) ] )
% 1.39/1.83 , clause( 2329, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'(
% 1.39/1.83 Z, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, T, X, X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ),
% 1.39/1.83 'c_Wellfounded_Oacc'( Z, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2330, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'(
% 1.39/1.83 Z, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, T, X, X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ),
% 1.39/1.83 'c_Wellfounded_Oacc'( Z, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2331, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_OImage'(
% 1.39/1.83 Z, T, U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( U, X ) ),
% 1.39/1.83 'c_Pair'( W, Y, U, X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W )
% 1.39/1.83 , T ) ) ) ] )
% 1.39/1.83 , clause( 2332, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_OImage'(
% 1.39/1.83 Z, T, U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( U, X ) ),
% 1.39/1.83 'c_Pair'( W, Y, U, X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W )
% 1.39/1.83 , T ) ) ) ] )
% 1.39/1.83 , clause( 2333, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ),
% 1.39/1.83 'c_Relation_OId__on'( Z, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2334, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Y, X, X ) ), 'c_Relation_OId__on'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.39/1.83 , clause( 2335, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( T, Y, X, X ) ), U ) )
% 1.39/1.83 ), ~( 'c_Equiv__Relations_Oequiv'( Z, U, X ) ) ] )
% 1.39/1.83 , clause( 2336, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ), U ) )
% 1.39/1.83 ), ~( 'c_Equiv__Relations_Oequiv'( Z, U, X ) ) ] )
% 1.39/1.83 , clause( 2337, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ORange'(
% 1.39/1.83 Z, T, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, X ) ),
% 1.39/1.83 'c_Pair'( U, Y, T, X ) ), Z ) ) ) ] )
% 1.39/1.83 , clause( 2338, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ORange'(
% 1.39/1.83 Z, T, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, X ) ),
% 1.39/1.83 'c_Pair'( U, Y, T, X ) ), Z ) ) ) ] )
% 1.39/1.83 , clause( 2339, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ODomain'(
% 1.39/1.83 Z, X, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, T ) ),
% 1.39/1.83 'c_Pair'( Y, U, X, T ) ), Z ) ) ) ] )
% 1.39/1.83 , clause( 2340, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ODomain'(
% 1.39/1.83 Z, X, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, T ) ),
% 1.39/1.83 'c_Pair'( Y, U, X, T ) ), Z ) ) ) ] )
% 1.39/1.83 , clause( 2341, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( Z, T ) ) ),
% 1.39/1.83 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( U, X ) ), 'c_Pair'( T, Y, U, X )
% 1.39/1.83 ), 'c_Product__Type_OSigma'( W, Z, U, X ) ) ) ) ] )
% 1.39/1.83 , clause( 2342, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, T ) ), 'c_Pair'( Y, U, X, T ) ),
% 1.39/1.83 'c_Product__Type_OSigma'( Z, W, X, T ) ) ) ) ] )
% 1.39/1.83 , clause( 2343, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.39/1.83 'c_Pair'( Z, Y, X, X ) ), T ) ), =( Z, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 X ), Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), U ) ) ), ~(
% 1.39/1.83 'c_Relation_Ototal__on'( U, T, X ) ) ] )
% 1.39/1.83 , clause( 2344, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Y, X, X ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ),
% 1.39/1.83 ~( 'c_Relation_Orefl__on'( T, Z, X ) ) ] )
% 1.39/1.83 , clause( 2345, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( T, Y, X, X ) ), U ) )
% 1.39/1.83 ), ~( 'c_Relation_Orefl__on'( Z, U, X ) ) ] )
% 1.39/1.83 , clause( 2346, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ), U ) )
% 1.39/1.83 ), ~( 'c_Relation_Orefl__on'( Z, U, X ) ) ] )
% 1.39/1.83 , clause( 2347, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Y, X, X ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ),
% 1.39/1.83 ~( 'c_Relation_Orefl__on'( T, Z, X ) ) ] )
% 1.39/1.83 , clause( 2348, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Wellfounded_Omlex__prod'( T, U, X ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( T, Y ) ), hAPP(
% 1.39/1.83 T, Z ) ) ) ) ] )
% 1.39/1.83 , clause( 2349, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'(
% 1.39/1.83 Y, Z, X, X ) ), 'c_Wellfounded_Omeasure'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( T, Y ) ), hAPP( T, Z )
% 1.39/1.83 ) ) ) ] )
% 1.39/1.83 , clause( 2350, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.39/1.83 , hAPP( X, Y ) ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( T, T ) ), 'c_Pair'( Y, Z, T, T ) ), 'c_Wellfounded_Omeasure'(
% 1.39/1.83 X, T ) ) ) ) ] )
% 1.39/1.83 , clause( 2351, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( 'v_c____', 'v_d____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( 'v_P____' ) ) ), ~( hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( 'v_c____', 'v_d____',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'v_F'( 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), hAPP( 'c_COMBC'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'v_h____', 'tc_nat',
% 1.39/1.83 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'v_n____' ),
% 1.39/1.83 'tc_bool', 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.83 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), hAPP( 'c_COMBC'(
% 1.39/1.83 'c_COMBB'( 'c_fequal'( 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'(
% 1.39/1.83 'tc_nat', 'tc_bool' ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'v_n____' ),
% 1.39/1.83 'tc_bool', 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'( hAPP( 'c_COMBC'(
% 1.39/1.83 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'v_c____' ), 'tc_Arrow__Order__Mirabelle_Oindi',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.83 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ) ) ] )
% 1.39/1.83 , clause( 2352, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( 'v_c____', 'v_d____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( 'c_COMBS'( 'c_COMBS'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'(
% 1.39/1.83 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_nat', 'tc_bool' ), 'v_n____' ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'(
% 1.39/1.83 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'v_e____' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 1.39/1.83 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ),
% 1.39/1.83 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_nat', 'tc_bool' ), 'v_n____' ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'(
% 1.39/1.83 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____'
% 1.39/1.83 , 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'v_c____' ), 'tc_Arrow__Order__Mirabelle_Oindi',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.83 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( 'v_c____', 'v_d____',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'v_F'( 'v_P____' ) ) ) ) ] )
% 1.39/1.83 , clause( 2353, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2354, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2355, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2356, [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2357, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( hAPP(
% 1.39/1.83 'c_Arrow__Order__Mirabelle_Omktop', Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , Z ) ) ), =( X, Y ), =( X, T ) ] )
% 1.39/1.83 , clause( 2358, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( hAPP(
% 1.39/1.83 'c_Arrow__Order__Mirabelle_Omktop', Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , Z ) ) ), =( Y, T ), =( X, T ) ] )
% 1.39/1.83 , clause( 2359, [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) )
% 1.39/1.83 , =( Y, W ) ] )
% 1.39/1.83 , clause( 2360, [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) )
% 1.39/1.83 , =( X, U ) ] )
% 1.39/1.83 , clause( 2361, [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( X, X, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( hAPP(
% 1.39/1.83 'c_Arrow__Order__Mirabelle_Omktop', Y ), X ) ) ) ) ] )
% 1.39/1.83 , clause( 2362, [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( hAPP(
% 1.39/1.83 'c_Arrow__Order__Mirabelle_Omktop', Z ), X ) ) ) ) ] )
% 1.39/1.83 , clause( 2363, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ] )
% 1.39/1.83 , clause( 2364, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Z, Y ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ] )
% 1.39/1.83 , clause( 2365, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), =( Z, Y ) ] )
% 1.39/1.83 , clause( 2366, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.39/1.83 , X ), Y ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y
% 1.39/1.83 ), X ) ), =( Y, X ) ] )
% 1.39/1.83 , clause( 2367, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), Y ) ) ] )
% 1.39/1.83 , clause( 2368, [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.39/1.83 , X ), Y ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y
% 1.39/1.83 ), X ) ), =( Y, X ) ] )
% 1.39/1.83 , clause( 2369, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ] )
% 1.39/1.83 , clause( 2370, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL(
% 1.39/1.83 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), =( Z, Y ) ] )
% 1.39/1.83 , clause( 2371, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), Z ) ), =( Y, T ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omktop', Z ), T ) ) ) ) ] )
% 1.39/1.83 , clause( 2372, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2373, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2374, [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2375, [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.39/1.83 ), X ), X ) ) ) ] )
% 1.39/1.83 , clause( 2376, [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.39/1.83 ), X ), X ) ) ) ] )
% 1.39/1.83 , clause( 2377, [ =( X, Y ), =( Y, X ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omkbot', Z ), X ) ) ) ] )
% 1.39/1.83 , clause( 2378, [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( X, X, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( hAPP(
% 1.39/1.83 'c_Arrow__Order__Mirabelle_Omkbot', Y ), X ) ) ) ) ] )
% 1.39/1.83 , clause( 2379, [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( hAPP(
% 1.39/1.83 'c_Arrow__Order__Mirabelle_Omkbot', Z ), Y ) ) ) ) ] )
% 1.39/1.83 , clause( 2380, [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ] )
% 1.39/1.83 , clause( 2381, [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ] )
% 1.39/1.83 , clause( 2382, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( hAPP(
% 1.39/1.83 'c_Arrow__Order__Mirabelle_Omkbot', Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , Z ) ) ), =( X, Y ), =( Y, T ) ] )
% 1.39/1.83 , clause( 2383, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( hAPP(
% 1.39/1.83 'c_Arrow__Order__Mirabelle_Omkbot', Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.39/1.83 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , Z ) ) ), =( X, T ), =( Y, T ) ] )
% 1.39/1.83 , clause( 2384, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.39/1.83 hAPP( Z, Y ) ) ) ] )
% 1.39/1.83 , clause( 2385, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.39/1.83 , Y ), X ) ) ) ] )
% 1.39/1.83 , clause( 2386, [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP(
% 1.39/1.83 Y, W ) ) ) ] )
% 1.39/1.83 , clause( 2387, [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP(
% 1.39/1.83 hAPP( X, W ), U ) ) ] )
% 1.39/1.83 , clause( 2388, [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X,
% 1.39/1.83 W ), hAPP( Y, W ) ) ) ] )
% 1.39/1.83 , clause( 2389, [ =( X, Y ), =( X, Y ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omktop', Z ), Y ) ) ) ] )
% 1.39/1.83 , clause( 2390, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), Z ) ), =( X, T ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omkbot', Z ), T ) ) ) ) ] )
% 1.39/1.83 , clause( 2391, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( 'v_a____', 'v_b____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( hAPP( 'c_COMBC'( hAPP(
% 1.39/1.83 'c_COMBC'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'(
% 1.39/1.83 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_nat', 'tc_bool' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.39/1.83 ), 'v_n____' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), 'tc_bool',
% 1.39/1.83 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'v_Lab____' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'v_Lba____' ) ) ) ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 2392, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( 'v_c____', 'v_e____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( 'c_COMBS'( 'c_COMBS'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'(
% 1.39/1.83 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_nat', 'tc_bool' ), 'v_n____' ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'(
% 1.39/1.83 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'v_e____' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 1.39/1.83 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ),
% 1.39/1.83 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_nat', 'tc_bool' ), 'v_n____' ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'(
% 1.39/1.83 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____'
% 1.39/1.83 , 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'v_c____' ), 'tc_Arrow__Order__Mirabelle_Oindi',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.83 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ), ~( hBOOL( hAPP(
% 1.39/1.83 hAPP( 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( 'v_a____', 'v_b____',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'v_F'( hAPP( 'c_COMBC'( hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_OIf'(
% 1.39/1.83 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), hAPP( 'c_COMBC'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'v_h____', 'tc_nat',
% 1.39/1.83 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), hAPP( hAPP(
% 1.39/1.83 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'v_n____' ),
% 1.39/1.83 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'v_Lab____' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'v_Lba____' ) ) ) ) )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2393, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( 'v_a____', 'v_b____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( hAPP( 'c_COMBC'( hAPP(
% 1.39/1.83 'c_COMBC'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'(
% 1.39/1.83 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_nat', 'tc_bool' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.39/1.83 ), 'v_n____' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), 'tc_bool',
% 1.39/1.83 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'v_Lab____' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'v_Lba____' ) ) ) ),
% 1.39/1.83 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( 'v_c____', 'v_e____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( 'c_COMBS'( 'c_COMBS'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'(
% 1.39/1.83 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_nat', 'tc_bool' ), 'v_n____' ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'(
% 1.39/1.83 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'v_e____' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 1.39/1.83 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ),
% 1.39/1.83 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_nat', 'tc_bool' ), 'v_n____' ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'(
% 1.39/1.83 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____'
% 1.39/1.83 , 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'v_c____' ), 'tc_Arrow__Order__Mirabelle_Oindi',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.83 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ) ) ] )
% 1.39/1.83 , clause( 2394, [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.83 , 'c_Pair'( 'v_c____', 'v_e____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( 'c_COMBS'( 'c_COMBS'(
% 1.39/1.83 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'(
% 1.39/1.83 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_nat', 'tc_bool' ), 'v_n____' ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'(
% 1.39/1.83 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'v_e____' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 1.39/1.83 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ),
% 1.39/1.83 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_nat', 'tc_bool' ), 'v_n____' ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'(
% 1.39/1.83 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____'
% 1.39/1.83 , 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), 'v_c____' ), 'tc_Arrow__Order__Mirabelle_Oindi',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ) ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.83 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.83 , 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.83 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.83 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.83 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ) ) ] )
% 1.39/1.83 , clause( 2395, [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_prod'( X, Y ) )
% 1.39/1.83 , ~( 'class_Finite__Set_Ofinite_Ofinite'( Y ) ), ~(
% 1.39/1.83 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ] )
% 1.39/1.83 , clause( 2396, [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) )
% 1.39/1.83 , ~( 'class_Lattices_Olattice'( Y ) ) ] )
% 1.39/1.83 , clause( 2397, [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) )
% 1.39/1.83 , ~( 'class_Lattices_Olattice'( Y ) ) ] )
% 1.39/1.83 , clause( 2398, [ 'class_Lattices_Odistrib__lattice'( 'tc_fun'( X, Y ) ),
% 1.39/1.83 ~( 'class_Lattices_Odistrib__lattice'( Y ) ) ] )
% 1.39/1.83 , clause( 2399, [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ),
% 1.39/1.83 ~( 'class_Lattices_Obounded__lattice'( Y ) ) ] )
% 1.39/1.83 , clause( 2400, [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ),
% 1.39/1.83 ~( 'class_Lattices_Oboolean__algebra'( Y ) ) ] )
% 1.39/1.83 , clause( 2401, [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_fun'( X, Y ) ),
% 1.39/1.83 ~( 'class_Finite__Set_Ofinite_Ofinite'( Y ) ), ~(
% 1.39/1.83 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ] )
% 1.39/1.83 , clause( 2402, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.39/1.83 'class_Orderings_Opreorder'( Y ) ) ] )
% 1.39/1.83 , clause( 2403, [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.39/1.83 'class_Lattices_Olattice'( Y ) ) ] )
% 1.39/1.83 , clause( 2404, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.39/1.83 'class_Orderings_Oorder'( Y ) ) ] )
% 1.39/1.83 , clause( 2405, [ 'class_Orderings_Otop'( 'tc_fun'( X, Y ) ), ~(
% 1.39/1.83 'class_Orderings_Otop'( Y ) ) ] )
% 1.39/1.83 , clause( 2406, [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~(
% 1.39/1.83 'class_Orderings_Obot'( Y ) ) ] )
% 1.39/1.83 , clause( 2407, [ 'class_HOL_Oord'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Oord'(
% 1.39/1.83 Y ) ) ] )
% 1.39/1.83 , clause( 2408, [
% 1.39/1.83 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 2409, [
% 1.39/1.83 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 1.39/1.83 )
% 1.39/1.83 , clause( 2410, [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.39/1.83 'tc_nat' ) ] )
% 1.39/1.83 , clause( 2411, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.39/1.83 'tc_nat' ) ] )
% 1.39/1.83 , clause( 2412, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.39/1.83 'tc_nat' ) ] )
% 1.39/1.83 , clause( 2413, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 1.39/1.83 'tc_nat' ) ] )
% 1.39/1.83 , clause( 2414, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 1.39/1.83 'tc_nat' ) ] )
% 1.39/1.83 , clause( 2415, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.39/1.83 'tc_nat' ) ] )
% 1.39/1.83 , clause( 2416, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2417, [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' )
% 1.39/1.83 ] )
% 1.39/1.83 , clause( 2418, [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ]
% 1.39/1.85 )
% 1.39/1.85 , clause( 2419, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 1.39/1.85 ] )
% 1.39/1.85 , clause( 2420, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 1.39/1.85 )
% 1.39/1.85 , clause( 2421, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ]
% 1.39/1.85 )
% 1.39/1.85 , clause( 2422, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 1.39/1.85 )
% 1.39/1.85 , clause( 2423, [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2424, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2425, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2426, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2427, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2428, [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2429, [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2430, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2431, [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2432, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2433, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2434, [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2435, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2436, [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2437, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2438, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2439, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2440, [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2441, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2442, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2443, [ 'class_Lattices_Olattice'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2444, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2445, [ 'class_Orderings_Obot'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2446, [ 'class_Power_Opower'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2447, [ 'class_HOL_Oord'( 'tc_nat' ) ] )
% 1.39/1.85 , clause( 2448, [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ] )
% 1.39/1.85 , clause( 2449, [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ] )
% 1.39/1.85 , clause( 2450, [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ] )
% 1.39/1.85 , clause( 2451, [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ] )
% 1.39/1.85 , clause( 2452, [ 'class_Lattices_Oboolean__algebra'( 'tc_bool' ) ] )
% 1.39/1.85 , clause( 2453, [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_bool' ) ] )
% 1.39/1.85 , clause( 2454, [ 'class_Orderings_Opreorder'( 'tc_bool' ) ] )
% 1.39/1.85 , clause( 2455, [ 'class_Lattices_Olattice'( 'tc_bool' ) ] )
% 1.39/1.85 , clause( 2456, [ 'class_Orderings_Oorder'( 'tc_bool' ) ] )
% 1.39/1.85 , clause( 2457, [ 'class_Orderings_Otop'( 'tc_bool' ) ] )
% 1.39/1.85 , clause( 2458, [ 'class_Orderings_Obot'( 'tc_bool' ) ] )
% 1.39/1.85 , clause( 2459, [ 'class_HOL_Oord'( 'tc_bool' ) ] )
% 1.39/1.85 , clause( 2460, [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X,
% 1.39/1.85 W ), hAPP( Y, W ) ) ) ] )
% 1.39/1.85 , clause( 2461, [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP(
% 1.39/1.85 hAPP( X, W ), U ) ) ] )
% 1.39/1.85 , clause( 2462, [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP(
% 1.39/1.85 Y, W ) ) ) ] )
% 1.39/1.85 , clause( 2463, [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ] )
% 1.39/1.85 , clause( 2464, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y
% 1.39/1.85 ) ) ) ] )
% 1.39/1.85 ] ).
% 1.39/1.85
% 1.39/1.85
% 1.39/1.85
% 1.39/1.85 subsumption(
% 1.39/1.85 clause( 1116, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.85 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.85 , 'c_Pair'( 'v_a____', 'v_b____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.85 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( hAPP( 'c_COMBC'( hAPP(
% 1.39/1.85 'c_COMBC'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.85 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.85 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'(
% 1.39/1.85 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.85 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.85 , 'tc_nat', 'tc_bool' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.39/1.85 ), 'v_n____' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), 'tc_bool',
% 1.39/1.85 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.86 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'v_Lab____' ),
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'v_Lba____' ) ) ) ) ]
% 1.39/1.86 )
% 1.39/1.86 , clause( 2391, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.86 , 'c_Pair'( 'v_a____', 'v_b____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( hAPP( 'c_COMBC'( hAPP(
% 1.39/1.86 'c_COMBC'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'(
% 1.39/1.86 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.86 , 'tc_nat', 'tc_bool' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.39/1.86 ), 'v_n____' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), 'tc_bool',
% 1.39/1.86 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.86 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'v_Lab____' ),
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'v_Lba____' ) ) ) ) ]
% 1.39/1.86 )
% 1.39/1.86 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.39/1.86
% 1.39/1.86
% 1.39/1.86
% 1.39/1.86 ==> clause( 1117, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.39/1.86 , 'c_Pair'( 'v_c____', 'v_e____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_F'( 'c_COMBS'( 'c_COMBS'(
% 1.39/1.86 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'(
% 1.39/1.86 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.86 , 'tc_nat', 'tc_bool' ), 'v_n____' ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.86 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.86 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'(
% 1.39/1.86 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 1.39/1.86 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'v_e____' ),
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 1.39/1.86 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ),
% 1.39/1.86 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.86 , 'tc_nat', 'tc_bool' ), 'v_n____' ), 'tc_bool', 'tc_fun'( 'tc_fun'(
% 1.39/1.86 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.86 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), hAPP( 'c_COMBC'(
% 1.39/1.86 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____'
% 1.39/1.86 , 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ),
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ) ) ), 'v_c____' ), 'tc_Arrow__Order__Mirabelle_Oindi',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.86 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.39/1.86 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ) ) ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.39/1.86 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ), 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 1.39/1.86 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oindi' ), 'tc_Arrow__Order__Mirabelle_Oindi'
% 1.39/1.86 , 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ) ), 'v_e____' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'(
% 1.39/1.86 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.39/1.86 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.39/1.86 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ) ] )
% 1.39/1.86
% 1.39/1.86
% 1.39/1.86
% 1.39/1.86 !!! Internal Problem: OH, OH, COULD NOT DERIVE GOAL !!!
% 1.39/1.86
% 1.39/1.86 Bliksem ended
%------------------------------------------------------------------------------