TSTP Solution File: SWV856-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV856-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:28:51 EDT 2022
% Result : Unsatisfiable 1.02s 1.43s
% Output : Refutation 1.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SWV856-1 : TPTP v8.1.0. Released v4.1.0.
% 0.05/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Wed Jun 15 21:46:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.02/1.42 *** allocated 10000 integers for termspace/termends
% 1.02/1.42 *** allocated 10000 integers for clauses
% 1.02/1.42 *** allocated 10000 integers for justifications
% 1.02/1.42 *** allocated 15000 integers for termspace/termends
% 1.02/1.42 Bliksem 1.12
% 1.02/1.42
% 1.02/1.42
% 1.02/1.42 Automatic Strategy Selection
% 1.02/1.42
% 1.02/1.42 Clauses:
% 1.02/1.42 [
% 1.02/1.42 [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z
% 1.02/1.42 , T ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y, U, 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ) ],
% 1.02/1.42 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X,
% 1.02/1.42 'c_Set_Oinsert'( U, Y, Z ), Z, T ) ) ],
% 1.02/1.42 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), 'c_lessequals'(
% 1.02/1.42 hAPP( Y, Z ), 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( T, Y
% 1.02/1.42 , U, X ), X ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( hAPP( X, Y ),
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, X, T, 'tc_fun'(
% 1.02/1.42 U, 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( T ), Y ), Z ) ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ), T,
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'(
% 1.02/1.42 Z, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.02/1.42 'c_Set_Oinsert'( T, X, Z ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.02/1.42 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofold1Set'( X, 'c_Set_Oinsert'( Y, Z, T ), U, T ),
% 1.02/1.42 hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), Z ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofold__graph'( X, Y, Z, U, T, T ) ) ],
% 1.02/1.42 [ =( hAPP( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( T, X, U, W, V0, V1
% 1.02/1.42 , V2, Z, Y ) ) ],
% 1.02/1.42 [ =( hAPP( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X, T, U, W, V0, V1
% 1.02/1.42 , Z, V2, Y ) ) ],
% 1.02/1.42 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.42 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool'
% 1.02/1.42 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), X ) ) ), hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( Z ), Y ), T ) ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'(
% 1.02/1.42 Y, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.02/1.42 , 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.42 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.42 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool'
% 1.02/1.42 ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), Z ) ) ],
% 1.02/1.42 [ =( 'c_Finite__Set_Ofold__image'( X, Y, Z, 'c_Set_Oimage'( T, U, W, V0
% 1.02/1.42 ), V1, V0 ), 'c_Finite__Set_Ofold__image'( X, 'c_Fun_Ocomp'( Y, T, V0,
% 1.02/1.42 V1, W ), Z, U, V1, W ) ), ~( 'c_Fun_Oinj__on'( T, U, W, V0 ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( U, W ) ), ~(
% 1.02/1.42 'c_OrderedGroup_Oab__semigroup__mult'( X, V1 ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 1.02/1.42 Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ),
% 1.02/1.42 'c_Finite__Set_Ofold'( 'c_Lattices_Oupper__semilattice__class_Osup'( X )
% 1.02/1.42 , Z, T, X, X ), X ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( T, X ) ) ],
% 1.02/1.42 [ 'c_Fun_Oinj__on'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T,
% 1.02/1.42 'tc_bool' ) ), T, U ), ~( 'c_Fun_Oinj__on'( X, Y, T, U ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), 'c_Set_Oinsert'( Y, Z, X ) ), T ), 'c_Set_Oinsert'( Y,
% 1.02/1.42 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ), Z ), T ), X ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, T, X ) ), 'c_Set_Oinsert'( Z,
% 1.02/1.42 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ), Y ), T ), X ) ) ],
% 1.02/1.42 [ =( 'c_Set_Ovimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T
% 1.02/1.42 , 'tc_bool' ) ), U, T ), 'c_HOL_Ominus__class_Ominus'( 'c_Set_Ovimage'( X
% 1.02/1.42 , Y, U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U, 'tc_bool' ) ) )
% 1.02/1.42 ],
% 1.02/1.42 [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.02/1.42 , 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.42 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.42 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool'
% 1.02/1.42 ) ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) )
% 1.02/1.42 ],
% 1.02/1.42 [ 'c_lessequals'( 'c_Set_Oimage'( X, 'c_Set_Ovimage'( X, Y, Z, T ), Z, T
% 1.02/1.42 ), Y, 'tc_fun'( T, 'tc_bool' ) ) ],
% 1.02/1.42 [ =( 'c_Set_Ovimage'( X, 'c_Set_Oimage'( X, Y, Z, T ), Z, T ), Y ), ~(
% 1.02/1.42 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), Z, T ) ) ],
% 1.02/1.42 [ =( 'c_Collect'( X, Y ), X ) ],
% 1.02/1.42 [ =( X, Y ), ~( 'c_Finite__Set_Ofold1Set'( Z, 'c_Set_Oinsert'( X,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), Y, T ) )
% 1.02/1.42 ],
% 1.02/1.42 [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.02/1.42 'tc_bool' ) ), Z, Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.02/1.42 'c_Complete__Lattice_OSup__class_OSup'( 'c_Set_Oinsert'( Y, Z, X ), X ),
% 1.02/1.42 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ),
% 1.02/1.42 'c_Complete__Lattice_OSup__class_OSup'( Z, X ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ),
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( X ) ), 'c_Orderings_Otop__class_Otop'( X
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( X ) ), Y ),
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool'
% 1.02/1.42 ) ) ), Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.02/1.42 ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' )
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 1.02/1.42 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ),
% 1.02/1.42 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.42 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 1.02/1.42 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.02/1.42 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'(
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ), Y ) ),
% 1.02/1.42 ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 1.02/1.42 Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), 'c_Set_Oinsert'( Y, Z, X ) ), 'c_Set_Oinsert'( Y, T, X
% 1.02/1.42 ) ), 'c_Set_Oinsert'( Y, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), X ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.02/1.42 'c_Set_Oinsert'( X, Y, Z ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( T ), Y ), U ) ) ), ~( 'c_Finite__Set_Ofinite'(
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( U, X, T, 'tc_fun'(
% 1.02/1.42 Z, 'tc_bool' ) ), Z ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( 'c_Set_Oinsert'( Z,
% 1.02/1.42 X, T ), Y ) ) ) ],
% 1.02/1.42 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z, T ) ) ),
% 1.02/1.42 ~( 'c_Fun_Oinj__on'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.42 , Y ), U ), Z, T ) ), =( Y, U ) ],
% 1.02/1.42 [ =( X, 'c_Set_Oinsert'(
% 1.02/1.42 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1'(
% 1.02/1.42 X, Y ),
% 1.02/1.42 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2'(
% 1.02/1.42 X, Y ), Y ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( hAPP( X, Y ), Z, 'tc_fun'( T, 'tc_bool' ) ), ~( hBOOL(
% 1.02/1.42 hAPP( hAPP( 'c_in'( U ), Y ), W ) ) ), ~( 'c_lessequals'(
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( W, X, U, 'tc_fun'(
% 1.02/1.42 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, X, Z ), 'tc_fun'( Z, 'tc_bool'
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ =( hAPP( 'c_Fun_Ocomp'( 'c_COMBK'( X, Y, Z ), T, Z, Y, 't_a' ), 'v_x'
% 1.02/1.42 ), X ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'(
% 1.02/1.42 'c_Set_Oinsert'( Z, X, Y ), Y ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( 'c_Set_Oinsert'( X, Y, Z ), Z ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), hAPP( Y, Z ) ),
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( T, Y, U, 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ) ), 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.42 T, Y, U, 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U )
% 1.02/1.42 , Z ), T ) ) ) ],
% 1.02/1.42 [ ~( =( hAPP( X,
% 1.02/1.42 'c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1'( Y, X
% 1.02/1.42 , Z, T ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) )
% 1.02/1.42 ), =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y, X, Z,
% 1.02/1.42 'tc_fun'( T, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofold__graph'( X, Y, Z, hAPP( hAPP( X, T ), U ), W, V0
% 1.02/1.42 ), ~( hBOOL( hAPP( hAPP( 'c_in'( W ), T ), Z ) ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofold__graph'( X, Y, 'c_HOL_Ominus__class_Ominus'( Z,
% 1.02/1.42 'c_Set_Oinsert'( T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( W,
% 1.02/1.42 'tc_bool' ) ), W ), 'tc_fun'( W, 'tc_bool' ) ), U, W, V0 ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oimage'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), Y, U ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.42 , 'c_Set_Oimage'( X, Z, Y, U ) ), 'c_Set_Oimage'( X, T, Y, U ) ) ), ~(
% 1.02/1.42 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.02/1.42 'tc_bool' ) ), Y, U ) ) ],
% 1.02/1.42 [ =( hAPP( X, 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( Z,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T ) ),
% 1.02/1.42 hAPP( hAPP( U, Y ), Z ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W
% 1.02/1.42 , X, V0, V1, V2, U, V3, V4, T ) ) ],
% 1.02/1.42 [ =( hAPP( X, 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( Z,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T ) ),
% 1.02/1.42 hAPP( hAPP( U, Y ), Z ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X
% 1.02/1.42 , W, V0, V1, U, V2, V3, V4, T ) ) ],
% 1.02/1.42 [ 'c_lessequals'( 'c_Set_Oimage'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), Y, U ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.42 , 'c_Set_Oimage'( X, Z, Y, U ) ), 'c_Set_Oimage'( X, T, Y, U ) ),
% 1.02/1.42 'tc_fun'( U, 'tc_bool' ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.02/1.42 [ 'c_lessequals'( 'c_Relation_OImage'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), Y, U ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.42 , 'c_Relation_OImage'( X, Z, Y, U ) ), 'c_Relation_OImage'( X, T, Y, U )
% 1.02/1.42 ), 'tc_fun'( U, 'tc_bool' ) ) ],
% 1.02/1.42 [ ~( =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ) ), T ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Z ), T ) ) ) ), 'c_lessequals'( T, Y, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ) ), T ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Z ), T ) ) ), ~( 'c_lessequals'( T, Y, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( hAPP( 'c_Map_Orestrict__map'( X, Y, Z, T ), U ),
% 1.02/1.42 'c_Option_Ooption_ONone'( T ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), Y )
% 1.02/1.42 ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ), =(
% 1.02/1.42 'c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1'( Y, Z, X ),
% 1.02/1.42 'c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2'( Y, Z, X ) )
% 1.02/1.42 ],
% 1.02/1.42 [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) )
% 1.02/1.42 ) ],
% 1.02/1.42 [ =( hAPP( X, hAPP( Y, Z ) ), hAPP( 'c_Fun_Ocomp'( X, Y, T, U, W ), Z )
% 1.02/1.42 ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) ) ), ~(
% 1.02/1.42 'c_Fun_Oinj__on'( U, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ), X, T ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), 'c_Set_Oimage'( Y, T,
% 1.02/1.42 U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ), ~(
% 1.02/1.42 'c_Fun_Oinj__on'( Y, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( U,
% 1.02/1.42 'tc_bool' ) ), U, X ) ) ],
% 1.02/1.42 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.02/1.42 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.02/1.42 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.02/1.42 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_OrderedGroup_Oab__semigroup__mult'( X
% 1.02/1.42 , U ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.02/1.42 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_OrderedGroup_Oab__semigroup__mult'( X
% 1.02/1.42 , U ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.02/1.42 'c_OrderedGroup_Oab__semigroup__mult'( X, T ) ) ],
% 1.02/1.42 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( 'c_Fun_Oinj__on'( X,
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( 'tc_fun'( T, 'tc_bool' ) ), T, U ) ), =(
% 1.02/1.42 Y, Z ) ],
% 1.02/1.42 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( T,
% 1.02/1.42 'tc_bool' ) ), Z ), X ), Y ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), T ) ), ~( hBOOL( hAPP( Z, T ) ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ hBOOL( hAPP( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.02/1.42 'c_Set_Oimage'( T, X, Z, U ), 'c_Set_Oimage'( T, Y, Z, U ), 'tc_fun'( U,
% 1.02/1.42 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( T, 'c_Orderings_Otop__class_Otop'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Z, U ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.02/1.42 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ), ~( 'c_lessequals'(
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.02/1.42 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.02/1.42 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ), ~( 'c_lessequals'(
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.02/1.42 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.02/1.42 Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( Z ), Y ), X ) ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y, T, Z
% 1.02/1.42 ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oimage'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), Y, U ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.42 , 'c_Set_Oimage'( X, Z, Y, U ) ), 'c_Set_Oimage'( X, T, Y, U ) ) ), ~(
% 1.02/1.42 'c_lessequals'( T, W, 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_lessequals'( Z
% 1.02/1.42 , W, 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, W, Y, U ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_lessequals'( X, 'c_Set_Oimage'(
% 1.02/1.42 Z, T, U, Y ), 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( T
% 1.02/1.42 , U ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( U ), Z ), W ) ) ), ~( 'c_lessequals'( 'c_Set_Oimage'( Y, W
% 1.02/1.42 , U, X ), T, 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ), 'c_Set_Oinsert'( X
% 1.02/1.42 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ), ~(
% 1.02/1.42 hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), T ) ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofold__graph'( Z, T
% 1.02/1.42 , X, U, Y, W ) ) ],
% 1.02/1.42 [ ~( =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( 't_a', X ) ), Y )
% 1.02/1.42 , Z ), 'v_x' ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 X ), hAPP( Y, 'v_x' ) ), hAPP( Z, 'v_x' ) ) ) ],
% 1.02/1.42 [ 'c_Fun_Oinj__on'( X, 'c_Set_Oimage'( Y, Z, T, U ), U, W ), ~(
% 1.02/1.42 'c_Fun_Oinj__on'( 'c_Fun_Ocomp'( X, Y, U, W, T ), Z, T, W ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ) ), T ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ), Y ), T ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), T ), 'c_Collect'( X, Z ) ) ) ) ) ],
% 1.02/1.42 [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Oid'( Y ), Y, Z, Y ), X ) ],
% 1.02/1.42 [ =( 'c_Fun_Ocomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( 'c_Set_Ovimage'( X, Y, Z, T ), Z ), ~(
% 1.02/1.42 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), Z, T ) ), ~( 'c_Finite__Set_Ofinite'( Y, T ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), Y ), Y ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Y ), Y ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.42 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.42 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( X, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.42 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.02/1.42 [ =( 'c_Relation_OImage'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), Y, U ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.42 , 'c_Relation_OImage'( X, Z, Y, U ) ), 'c_Relation_OImage'( X, T, Y, U )
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ 'c_Fun_Oinj__on'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U ), hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( U ), hAPP( X, Y ) ), 'c_Set_Oimage'( X,
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( Z, 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.02/1.42 T, 'tc_bool' ) ), T, U ) ) ), ~( 'c_Fun_Oinj__on'( X, Z, T, U ) ) ],
% 1.02/1.42 [ 'c_Fun_Oinj__on'( 'c_Fun_Oid'( X ), Y, X, X ) ],
% 1.02/1.42 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 1.02/1.42 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Z, Y,
% 1.02/1.42 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), X ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP( hAPP( X, W ),
% 1.02/1.42 U ) ) ],
% 1.02/1.42 [ =( hAPP( 'c_COMBK'( X, Y, Z ), T ), X ) ],
% 1.02/1.42 [ ~( =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), 'c_Set_Oimage'( Y,
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( U, 'tc_bool' ) ), U, X ) )
% 1.02/1.42 , 'c_Set_Oimage'( Y, 'c_HOL_Ominus__class_Ominus'( T, Z, 'tc_fun'( U,
% 1.02/1.42 'tc_bool' ) ), U, X ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ), ~( 'c_Fun_Oinj__on'( Y, T, U, X ) ), ~(
% 1.02/1.42 'c_Fun_Oinj__on'( Y, Z, U, X ) ), 'c_Fun_Oinj__on'( Y, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), U, X ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), 'c_Set_Oimage'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 1.02/1.42 'tc_fun'( U, 'tc_bool' ) ), U, X ) ), 'c_Set_Oimage'( Y,
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( T, Z, 'tc_fun'( U, 'tc_bool' ) ), U, X ) )
% 1.02/1.42 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.02/1.42 'c_Fun_Oinj__on'( Y, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), U, X ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.42 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.02/1.42 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.02/1.42 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.02/1.42 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.02/1.42 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.42 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.02/1.42 [ ~( 'class_HOL_Oord'( X ) ), ~( 'c_lessequals'( Y, Z, 'tc_fun'( T, X )
% 1.02/1.42 ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_fun'( T, X ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.02/1.42 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), 'c_Set_Oimage'( Y,
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( 'tc_fun'( T, 'tc_bool' ) ), T, X ) ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.02/1.42 'c_Complete__Lattice_OSup__class_OSup'( Y, X ), 'c_Finite__Set_Ofold'(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( X ), Y, X, X ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.02/1.42 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.02/1.42 , T, X ) ) ), =( Y, Z ) ],
% 1.02/1.42 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.02/1.42 , T, X ) ) ), =( Z, T ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.42 'c_Finite__Set_Olinorder__class_OMax'( Y, X ),
% 1.02/1.42 'c_Finite__Set_Olinorder__class_OMax'( Z, X ), X ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_lessequals'( Y, Z, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.42 'c_Finite__Set_Olinorder__class_OMax'( 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X ), Y )
% 1.02/1.42 ],
% 1.02/1.42 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oimage'( X, Y, Z
% 1.02/1.42 , T ), 'c_Set_Oimage'( X, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.02/1.42 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, U, 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), T ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ) ), T ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Z ), T ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), Z ), Y ), ~( 'c_lessequals'( Y, Z, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), Z ), Z ), ~( 'c_lessequals'( Z, Y, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Y ), ~(
% 1.02/1.42 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Y ) ),
% 1.02/1.42 'c_lessequals'( Y, Z, X ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Z ), ~(
% 1.02/1.42 'c_lessequals'( Z, Y, X ) ) ],
% 1.02/1.42 [ 'c_lessequals'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ), ~( 'c_lessequals'( Z, T,
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , Z ), X ), 'tc_fun'( Y, 'tc_bool' ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , X ), Z ), 'tc_fun'( Y, 'tc_bool' ) ) ],
% 1.02/1.42 [ 'c_lessequals'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ), ~( 'c_lessequals'( Z, T,
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), T, X )
% 1.02/1.42 , ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.02/1.42 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ),
% 1.02/1.42 X ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.02/1.42 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ),
% 1.02/1.42 X ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), T, X )
% 1.02/1.42 , ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), T, X )
% 1.02/1.42 , ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ), X ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), X ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), Y ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), Y ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), Y ) ) ],
% 1.02/1.42 [ 'c_Complete__Lattice_Ocomplete__lattice'( X, Y, 'c_COMBC'( Z, T, T,
% 1.02/1.42 'tc_bool' ), 'c_COMBC'( U, T, T, 'tc_bool' ), W, V0, V1, V2, T ), ~(
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice'( Y, X, Z, U, V0, W, V2, V1, T )
% 1.02/1.42 ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ), Z ), ~( 'c_lessequals'( Y, Z, 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), X ) ],
% 1.02/1.42 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 1.02/1.42 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'c_Set_Oinsert'( X,
% 1.02/1.42 Y, Z ) ) ],
% 1.02/1.42 [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.02/1.42 , 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 1.02/1.42 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.42 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.42 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool'
% 1.02/1.42 ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), Z ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ) ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ) ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), T ), Y ) ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z, Y ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofold__graph'( X, Y, 'c_Set_Oinsert'( Z, T, U ), hAPP(
% 1.02/1.42 hAPP( X, Y ), W ), U, U ), hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ),
% 1.02/1.42 ~( 'c_Finite__Set_Ofold__graph'( X, Z, T, W, U, U ) ), ~(
% 1.02/1.42 'c_OrderedGroup_Oab__semigroup__mult'( X, U ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T
% 1.02/1.42 , 'tc_bool' ) ), T, U ), 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oimage'( X
% 1.02/1.42 , Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ),
% 1.02/1.42 ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( T,
% 1.02/1.42 'tc_bool' ) ), T, U ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 1.02/1.42 'c_Set_Oinsert'( Y, T, X ), Z, 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y, 'c_COMBK'( Z, X
% 1.02/1.42 , T ), T, X ), Z ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL( hAPP( Y, T )
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ),
% 1.02/1.42 'c_Set_Oimage'( X, Z, T, U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), Z
% 1.02/1.42 ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.02/1.42 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( T ), Y ), X ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( Z ), T ), X ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( T, Y, Z )
% 1.02/1.42 , 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.02/1.42 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( T ), Y ), X ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 1.02/1.42 , 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( Z ), T ), X ) ) ],
% 1.02/1.42 [ 'c_lessequals'( 'c_Set_Ovimage'( X, Y, Z, T ), 'c_Set_Ovimage'( X, U,
% 1.02/1.42 Z, T ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, U, 'tc_fun'( T
% 1.02/1.42 , 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, T, X ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), 'c_Set_Oinsert'( Y, Z, X ) ), T ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ],
% 1.02/1.42 [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( 'c_Fun_Oid'( T )
% 1.02/1.42 , W, T, T, U ) ) ), =( hAPP( X, hAPP( Y, V0 ) ), hAPP( W, V0 ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ), Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oimage'( X, Y, Z, Z ), Y ), ~( 'c_Fun_Oinj__on'( X, Y, Z, Z
% 1.02/1.42 ) ), ~( 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, Z ), Y, 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.02/1.42 [ ~( =( hAPP( X,
% 1.02/1.42 'c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1'( Y, X
% 1.02/1.42 , Z, T ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) )
% 1.02/1.42 ), =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ),
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y, X, Z, 'tc_fun'(
% 1.02/1.42 T, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ) ), T ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Z ), T ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), T ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.42 'c_Finite__Set_Olinorder__class_OMin'( 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X ), Y )
% 1.02/1.42 ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'( hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y,
% 1.02/1.42 'tc_bool' ) ), X ), Z ), Y ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'( hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y,
% 1.02/1.42 'tc_bool' ) ), Z ), X ), Y ) ) ],
% 1.02/1.42 [ =( 'c_Map_Orestrict__map'( 'c_Map_Orestrict__map'( X, Y, Z, T ), U, Z
% 1.02/1.42 , T ), 'c_Map_Orestrict__map'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.42 , Y ), U ), Z, T ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Z, Y,
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ), T ), T ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ),
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), T, Z,
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ), Y ) ],
% 1.02/1.42 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z, T ) ) ),
% 1.02/1.42 ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), Z, T ) ), =( Y, U ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ),
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( X ) ) ), =( Z,
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ),
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( X ) ) ), =( Y,
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( Z ), T ), X ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), Y ) ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.02/1.42 , 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 1.02/1.42 hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ), hBOOL( hAPP( hAPP( 'c_in'( T
% 1.02/1.42 ), Y ), Z ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), T ), 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), T ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Z ), T ), 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ), 'c_Set_Oinsert'( X
% 1.02/1.42 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ), =( T
% 1.02/1.42 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( hBOOL(
% 1.02/1.42 hAPP( hAPP( 'c_in'( Z ), T ), Y ) ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.02/1.42 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.02/1.42 , 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), Z ) ) ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.02/1.42 'c_Finite__Set_Ofold'( 'c_Lattices_Olower__semilattice__class_Oinf'( X )
% 1.02/1.42 , Y, 'c_Set_Oinsert'( Z, T, X ), X, X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ),
% 1.02/1.42 'c_Finite__Set_Ofold'( 'c_Lattices_Olower__semilattice__class_Oinf'( X )
% 1.02/1.42 , Y, T, X, X ) ) ), ~( 'c_Finite__Set_Ofinite'( T, X ) ) ],
% 1.02/1.42 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( T, U, 'tc_fun'( Z, 'tc_bool'
% 1.02/1.42 ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( U, Y, 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ),
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( X ) ), Y ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ),
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( X ) ), Y ), Y ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool'
% 1.02/1.42 ) ) ), Y ), Y ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ), Y ) ],
% 1.02/1.42 [ =( 'c_Set_Oimage'( X, 'c_Set_Ovimage'( X, Y, Z, T ), Z, T ), hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( T,
% 1.02/1.42 'tc_bool' ) ), Y ), 'c_Set_Oimage'( X, 'c_Orderings_Otop__class_Otop'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ), X ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), T ), Z ), 'tc_fun'( X, 'tc_bool' ) ),
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.42 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.42 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_HOL_Oord'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_fun'(
% 1.02/1.42 T, X ) ), 'c_lessequals'( Z, Y, 'tc_fun'( T, X ) ), ~( 'c_lessequals'( Y
% 1.02/1.42 , Z, 'tc_fun'( T, X ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.02/1.42 , X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.02/1.42 , Y, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.02/1.42 , Y, X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), Y ) ],
% 1.02/1.42 [ hBOOL( hAPP( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' )
% 1.02/1.42 ), Y ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Otop'( X ) ), =( hAPP(
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.02/1.42 hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z, 'tc_bool' ), 'tc_bool' ), X
% 1.02/1.42 ), hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z, 'tc_bool' ), 'tc_bool'
% 1.02/1.42 ), Y ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ), 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ), 'tc_bool' ), Z ), 'tc_fun'( X, 'tc_bool' ) ), ~(
% 1.02/1.42 'c_lessequals'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.02/1.42 'c_Finite__Set_Ofold'( 'c_Lattices_Oupper__semilattice__class_Osup'( X )
% 1.02/1.42 , Y, 'c_Set_Oinsert'( Z, T, X ), X, X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ),
% 1.02/1.42 'c_Finite__Set_Ofold'( 'c_Lattices_Oupper__semilattice__class_Osup'( X )
% 1.02/1.42 , Y, T, X, X ) ) ), ~( 'c_Finite__Set_Ofinite'( T, X ) ) ],
% 1.02/1.42 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.02/1.42 ), =( Z, Y ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.42 ) ],
% 1.02/1.42 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.02/1.42 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.02/1.42 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.02/1.42 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.42 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.02/1.42 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.02/1.42 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.42 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.02/1.42 ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), Y ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.42 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), T, X ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.42 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), T, X ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ), Y ) ],
% 1.02/1.42 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( Y, Z, 'tc_fun'( T, X ) ),
% 1.02/1.42 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_fun'( T, X ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), Y ), ~(
% 1.02/1.42 'c_lessequals'( Z, Y, X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), Z ) ),
% 1.02/1.42 'c_lessequals'( Y, Z, X ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), Z ), ~(
% 1.02/1.42 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), Z ), Z ), ~( 'c_lessequals'( Y, Z, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), Z ), Y ), ~( 'c_lessequals'( Z, Y, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), Z ) ), 'c_lessequals'( Y, Z,
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( 'c_Set_Oimage'( X, Y, Z, T ), T ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.02/1.42 [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.02/1.42 , 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 1.02/1.42 hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.42 X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.42 'c_Finite__Set_Olinorder__class_OMin'( Y, X ),
% 1.02/1.42 'c_Finite__Set_Olinorder__class_OMin'( Z, X ), X ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( Y, X ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_lessequals'( Z, Y, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.42 'c_Set_Oinsert'( X, Y, Z ), T, Z, 'tc_fun'( U, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.42 , hAPP( T, X ) ), 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.42 Y, T, Z, 'tc_fun'( U, 'tc_bool' ) ) ) ) ],
% 1.02/1.42 [ =( hAPP( X, 'c_Set_Oinsert'( Y, Z, T ) ), hAPP( hAPP( U, Y ), hAPP( X
% 1.02/1.42 , Z ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W, X, V0, V1, V2
% 1.02/1.42 , U, V3, V4, T ) ) ],
% 1.02/1.42 [ =( hAPP( X, 'c_Set_Oinsert'( Y, Z, T ) ), hAPP( hAPP( U, Y ), hAPP( X
% 1.02/1.42 , Z ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X, W, V0, V1, U,
% 1.02/1.42 V2, V3, V4, T ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofold1Set'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y, Z ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 1.02/1.42 'c_Hoare__Mirabelle_Ohoare__derivs'( X, T, Z ) ), ~(
% 1.02/1.42 'c_Hoare__Mirabelle_Ohoare__derivs'( T, Y, Z ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), 'c_Set_Oinsert'( Y, Z, X ) ), T ), 'c_Set_Oinsert'( Y,
% 1.02/1.42 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ), Z ), T ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T
% 1.02/1.42 ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, T, X ) ), 'c_Set_Oinsert'( Z,
% 1.02/1.42 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ), Y ), T ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y
% 1.02/1.42 ) ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oimage'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U ),
% 1.02/1.42 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Orderings_Otop__class_Otop'(
% 1.02/1.42 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W ), hAPP( Y, hAPP( X, W ) )
% 1.02/1.42 ) ],
% 1.02/1.42 [ 'c_lessequals'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), T ), U ), 'tc_fun'( X, 'tc_bool' ) ), ~(
% 1.02/1.42 'c_lessequals'( Z, U, 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_lessequals'( Y
% 1.02/1.42 , T, 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Y, X ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Z, X ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.02/1.42 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ),
% 1.02/1.42 X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.02/1.42 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ),
% 1.02/1.42 X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.02/1.42 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ),
% 1.02/1.42 X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Z, X )
% 1.02/1.42 ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Y, X )
% 1.02/1.42 ],
% 1.02/1.42 [ 'c_lessequals'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), Y, 'tc_fun'( X, 'tc_bool' ) ) ],
% 1.02/1.42 [ 'c_lessequals'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), Z, 'tc_fun'( X, 'tc_bool' ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'( X, T, 'tc_fun'(
% 1.02/1.42 Y, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) )
% 1.02/1.42 ],
% 1.02/1.42 [ 'c_lessequals'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'( X, T, 'tc_fun'(
% 1.02/1.42 Y, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) )
% 1.02/1.42 ],
% 1.02/1.42 [ 'c_lessequals'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.02/1.42 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Otop'( X ) ), 'c_lessequals'( Y,
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( X ), X ) ],
% 1.02/1.42 [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Ocomp'( Y, Z, T, U, W ), U, V0, W ),
% 1.02/1.42 'c_Fun_Ocomp'( 'c_Fun_Ocomp'( X, Y, U, V0, T ), Z, T, V0, W ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oinsert'( X,
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Z, Y,
% 1.02/1.42 'tc_fun'( T, 'tc_bool' ) ), T ), 'c_Set_Oinsert'( X,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ],
% 1.02/1.42 [ ~( 'class_HOL_Ominus'( X ) ), =( hAPP( 'c_HOL_Ominus__class_Ominus'( Y
% 1.02/1.42 , Z, 'tc_fun'( 't_a', X ) ), 'v_x' ), 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.02/1.42 Y, 'v_x' ), hAPP( Z, 'v_x' ), X ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 1.02/1.42 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), T ), Y ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 1.02/1.42 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), Y ), T ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.02/1.42 X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ), X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.02/1.42 X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), T ), Z ), X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), T, X )
% 1.02/1.42 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), T, X )
% 1.02/1.42 , ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.02/1.42 X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ), X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.02/1.42 X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), T ), Z ), X ) ) ],
% 1.02/1.42 [ =( 'c_Set_Ovimage'( 'c_Fun_Oid'( X ), Y, X, X ), Y ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.02/1.42 'c_Finite__Set_Ofold'( 'c_Lattices_Olower__semilattice__class_Oinf'( X )
% 1.02/1.42 , Y, Z, X, X ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 X ), T ), Y ), X ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Z ) ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.02/1.42 [ =( 'c_Set_Ovimage'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U, T ),
% 1.02/1.42 'c_Set_Ovimage'( Y, 'c_Set_Ovimage'( X, W, Z, T ), U, Z ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oinsert'( X, Y, Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.42 , 'c_Collect'( hAPP( 'c_COMBC'( 'c_fequal'( Z ), Z, Z, 'tc_bool' ), X ),
% 1.02/1.42 Z ) ), Y ) ) ],
% 1.02/1.42 [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.02/1.42 , 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 1.02/1.42 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.42 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.42 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool'
% 1.02/1.42 ) ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) )
% 1.02/1.42 ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), Y ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oimage'( 'c_Fun_Oid'( X ), Y, X, X ), Y ) ],
% 1.02/1.42 [ =( 'c_Set_Oinsert'( X, Y, Z ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.42 , 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), Z ) ), Y ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofold__graph'( X, Y, 'c_Set_Oinsert'( Z,
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( T, 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ), U ), 'tc_fun'(
% 1.02/1.42 U, 'tc_bool' ) ), U ), W, U, U ), hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T
% 1.02/1.42 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Y ), T ) ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofold__graph'( X, Z, T, W, U, U ) ), ~(
% 1.02/1.42 'c_OrderedGroup_Oab__semigroup__mult'( X, U ) ) ],
% 1.02/1.42 [ 'c_Fun_Oinj__on'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U, T ), ~(
% 1.02/1.42 'c_Fun_Oinj__on'( X, 'c_Set_Oimage'( Y, W, U, Z ), Z, T ) ), ~(
% 1.02/1.42 'c_Fun_Oinj__on'( Y, W, U, Z ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' )
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ), 'c_Finite__Set_Ofinite'(
% 1.02/1.42 Y, X ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofold__graph'( X, Y, 'c_Set_Oinsert'( Z, T, U ), hAPP(
% 1.02/1.42 hAPP( X, Z ), W ), U, V0 ), ~( 'c_Finite__Set_Ofold__graph'( X, Y, T, W,
% 1.02/1.42 U, V0 ) ), hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), 'c_Collect'( T, X ) ) ) ) ) ],
% 1.02/1.42 [ =( 'c_Set_Ovimage'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), U, Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.42 , 'c_Set_Ovimage'( X, Z, U, Y ) ), 'c_Set_Ovimage'( X, T, U, Y ) ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.02/1.42 'c_Complete__Lattice_OSup__class_OSup'( 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ), X ), X ), X ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ],
% 1.02/1.42 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), 'c_Set_Oimage'( Y,
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( T, 'c_Set_Oinsert'( Z,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ), U ), 'tc_fun'(
% 1.02/1.42 U, 'tc_bool' ) ), U, X ) ) ) ), ~( 'c_Fun_Oinj__on'( Y, 'c_Set_Oinsert'(
% 1.02/1.42 Z, T, U ), U, X ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ), T,
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), Z ) ),
% 1.02/1.42 hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ],
% 1.02/1.42 [ 'c_Nitpick_Ofold__graph_H'( X, Y, Z, hAPP( hAPP( X, T ), U ), W, V0 )
% 1.02/1.42 , ~( 'c_Nitpick_Ofold__graph_H'( X, Y, 'c_HOL_Ominus__class_Ominus'( Z,
% 1.02/1.42 'c_Set_Oinsert'( T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( W,
% 1.02/1.42 'tc_bool' ) ), W ), 'tc_fun'( W, 'tc_bool' ) ), U, W, V0 ) ), ~( hBOOL(
% 1.02/1.42 hAPP( hAPP( 'c_in'( W ), T ), Z ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 1.02/1.42 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~(
% 1.02/1.42 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.02/1.42 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.42 , T ), X ), Y ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.42 , X ), T ), Y ) ) ) ],
% 1.02/1.42 [ 'c_Fun_Oinj__on'( X, Y, Z, Z ), ~( 'c_lessequals'( Y, 'c_Set_Oimage'(
% 1.02/1.42 X, Y, Z, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y
% 1.02/1.42 , Z ) ) ],
% 1.02/1.42 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.42 , U ), Y ), Z, T ) ) ],
% 1.02/1.42 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.42 , Y ), U ), Z, T ) ) ],
% 1.02/1.42 [ 'c_lessequals'( 'c_Set_Ovimage'( X, Y, Z, T ), U, 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), ~( 'c_lessequals'( Y, 'c_Set_Oimage'( X, U, Z, T ),
% 1.02/1.42 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X,
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.02/1.42 'c_Complete__Lattice_OSup__class_OSup'( 'c_Orderings_Otop__class_Otop'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), X ), 'c_Orderings_Otop__class_Otop'( X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ =( hAPP( 'c_Fun_Oid'( X ), Y ), Y ) ],
% 1.02/1.42 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X, hAPP(
% 1.02/1.42 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), Y ), T ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ), T,
% 1.02/1.42 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( X, 't_a' ), ~( 'c_Wellfounded_Omax__extp'( Y
% 1.02/1.42 , Z, X, 't_a' ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( X, 't_a' ), ~( 'c_Wellfounded_Omax__extp'( Y
% 1.02/1.42 , X, Z, 't_a' ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ), X ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ), X ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.42 [ =( 'c_Set_Ovimage'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), U, Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.42 , 'c_Set_Ovimage'( X, Z, U, Y ) ), 'c_Set_Ovimage'( X, T, U, Y ) ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.02/1.42 [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( hAPP( Y, Z ), hAPP( T, Z )
% 1.02/1.42 , X ), ~( 'c_lessequals'( Y, T, 'tc_fun'( U, X ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( hBOOL(
% 1.02/1.42 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( hBOOL(
% 1.02/1.42 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T, X ) ) ),
% 1.02/1.42 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T, X ) ) ),
% 1.02/1.42 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( 'c_lessequals'( T, Z,
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T )
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.02/1.42 [ =( hAPP( 'c_Map_Orestrict__map'( X, Y, Z, T ), U ), hAPP( X, U ) ),
% 1.02/1.42 ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), Y ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), =( Y, T ), ~( hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( T, Z, X ) ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.02/1.42 X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , T ), Z ) ) ) ) ],
% 1.02/1.42 [ =( hAPP( 'c_Fun_Ooverride__on'( X, Y, Z, T, U ), W ), hAPP( Y, W ) ),
% 1.02/1.42 ~( hBOOL( hAPP( hAPP( 'c_in'( T ), W ), Z ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Otop__class_Otop'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.02/1.42 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( T, Z, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ) ) ],
% 1.02/1.42 [ =( hAPP( 'c_Fun_Ooverride__on'( X, Y, Z, T, U ), W ), hAPP( X, W ) ),
% 1.02/1.42 hBOOL( hAPP( hAPP( 'c_in'( T ), W ), Z ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( X ), Y ), T ) ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , T ), Z ) ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ) ) ) ) ],
% 1.02/1.42 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T
% 1.02/1.42 ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), U ) ) ), =( Y,
% 1.02/1.42 Z ), ~( 'c_Fun_Oinj__on'( X, U, T, W ) ) ],
% 1.02/1.42 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T
% 1.02/1.42 ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), U ) ) ), ~(
% 1.02/1.42 'c_Fun_Oinj__on'( X, U, T, W ) ), =( Y, Z ) ],
% 1.02/1.42 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T
% 1.02/1.42 ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), U ) ) ), ~(
% 1.02/1.42 'c_Fun_Oinj__on'( X, U, T, W ) ), =( Y, Z ) ],
% 1.02/1.42 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( 'c_Fun_Oinj__on'( X, T, U, W
% 1.02/1.42 ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ), ~(
% 1.02/1.42 hBOOL( hAPP( hAPP( 'c_in'( U ), Y ), T ) ) ) ],
% 1.02/1.42 [ ~( =( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool' ),
% 1.02/1.42 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool'
% 1.02/1.42 ), 'tc_bool' ), Z ) ) ), =( Y, Z ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Collect'( Z, X ) ) ), ~( hBOOL(
% 1.02/1.42 hAPP( Z, Y ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.02/1.42 'c_Collect'( X, Z ) ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.02/1.42 T, 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T
% 1.02/1.42 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.02/1.42 T, 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T
% 1.02/1.42 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.02/1.42 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z ) ) ),
% 1.02/1.42 hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( Z
% 1.02/1.42 ), X ), Y ) ), =( Y, T ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, T, U, 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( T, W
% 1.02/1.42 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), Z ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, T, U, 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( T, W
% 1.02/1.42 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), Z ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.02/1.42 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.02/1.42 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.02/1.42 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( U ), T ), Z ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( Y
% 1.02/1.42 , W, X, V0, V1, V2, V3, V4, U ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( U ), Y ), T ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W
% 1.02/1.42 , Z, X, V0, V1, V2, V3, V4, U ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.02/1.42 , X ), Y ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X
% 1.02/1.42 , Y, Z, 'tc_fun'( T, 'tc_bool' ) ), U ) ), ~( hBOOL( hAPP( hAPP( Y, W ),
% 1.02/1.42 U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), W ), X ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X
% 1.02/1.42 , Y, Z, 'tc_fun'( T, 'tc_bool' ) ), U ) ), ~( hBOOL( hAPP( hAPP( Y, W ),
% 1.02/1.42 U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), W ), X ) ) ) ],
% 1.02/1.42 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ) ), T ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ), Y ), T ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ],
% 1.02/1.42 [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool'
% 1.02/1.42 ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( hBOOL(
% 1.02/1.42 hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( X, Y ), hAPP( Z, T ) ), 'c_Finite__Set_Ofold'( X, Y, T
% 1.02/1.42 , U, U ) ), ~( 'c_Finite__Set_Ofinite'( T, U ) ), ~(
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice'( W, Z, V0, V1, V2, X, V3, V4, U
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( X, Y ), hAPP( Z, T ) ), 'c_Finite__Set_Ofold'( X, Y, T
% 1.02/1.42 , U, U ) ), ~( 'c_Finite__Set_Ofinite'( T, U ) ), ~(
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice'( Z, W, V0, V1, X, V2, V3, V4, U
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ =( hAPP( X, Y ), 'c_Finite__Set_Ofold'( Z, T, Y, U, U ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( Y, U ) ), ~(
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice'( W, X, V0, V1, V2, Z, T, V3, U )
% 1.02/1.42 ) ],
% 1.02/1.42 [ =( hAPP( X, Y ), 'c_Finite__Set_Ofold'( Z, T, Y, U, U ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( Y, U ) ), ~(
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice'( X, W, V0, V1, Z, V2, V3, T, U )
% 1.02/1.42 ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 1.02/1.42 Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'(
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z
% 1.02/1.42 , 'tc_bool' ) ), Z ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.42 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), T ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T
% 1.02/1.42 , 'tc_bool' ) ), T ) ) ],
% 1.02/1.42 [ =( 'c_Fun_Ofcomp'( X, 'c_Fun_Oid'( Y ), Z, Y, Y ), X ) ],
% 1.02/1.42 [ =( 'c_Fun_Ofcomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y ) ],
% 1.02/1.42 [ =( 'c_Set_Oimage'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U, T ),
% 1.02/1.42 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, W, U, Z ), Z, T ) ) ],
% 1.02/1.42 [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ), 'c_Finite__Set_Ofinite'(
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X ) ],
% 1.02/1.42 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.02/1.42 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.02/1.42 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ),
% 1.02/1.42 'c_Complete__Lattice_OSup__class_OSup'( Z, X ) ), 'c_Finite__Set_Ofold'(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y, Z, X, X ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Y ), Y ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), Y ), Y ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.02/1.42 X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), T ), Y ), Z, X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.02/1.42 X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ), Z, X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.02/1.42 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ),
% 1.02/1.42 X ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.02/1.42 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ),
% 1.02/1.42 X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.02/1.42 X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), T ), Y ), Z, X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.02/1.42 X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ), Z, X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.02/1.42 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), X ), T ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.02/1.42 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), T ), X ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( 't_a', X ) ), Y )
% 1.02/1.42 , Z ), 'v_x' ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 X ), hAPP( Y, 'v_x' ) ), hAPP( Z, 'v_x' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.42 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.42 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.42 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.42 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ],
% 1.02/1.42 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( T
% 1.02/1.42 , Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_lessequals'( Y, U, 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, U, Z, T ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( Z, Y ) ) ), ~( 'c_lessequals'(
% 1.02/1.42 Z, X, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) )
% 1.02/1.42 , ~( 'c_lessequals'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.42 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( X, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.02/1.42 'c_lessequals'( X, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( X, Y ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( T, 'tc_bool'
% 1.02/1.42 ) ) ), ~( hBOOL( hAPP( Z, Y ) ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_lessequals'( X, Z, 'tc_fun'( Y
% 1.02/1.42 , 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.42 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.02/1.42 , X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.42 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.02/1.42 , X ) ) ],
% 1.02/1.42 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.02/1.42 'c_Complete__Lattice_OSup__class_OSup'( 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X ), Y )
% 1.02/1.42 ],
% 1.02/1.42 [ 'c_lessequals'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), T ), U ), 'tc_fun'( X, 'tc_bool' ) ), ~(
% 1.02/1.42 'c_lessequals'( Z, U, 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_lessequals'( Y
% 1.02/1.42 , T, 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Y, 'tc_bool' ) ) ) ) ],
% 1.02/1.42 [ =( 'c_Collect'( hAPP( 'c_COMBC'( 'c_fequal'( X ), X, X, 'tc_bool' ), Y
% 1.02/1.42 ), X ), 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X
% 1.02/1.42 , 'tc_bool' ) ), X ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) )
% 1.02/1.42 ],
% 1.02/1.42 [ =( 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T
% 1.02/1.42 , 'tc_bool' ) ), T, U ), 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oimage'( X
% 1.02/1.42 , Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ),
% 1.02/1.42 ~( 'c_lessequals'( Z, W, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'(
% 1.02/1.42 Y, W, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, W, T, U ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ =( hAPP( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), Y ), ~(
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice'( T, X, U, W, V0, V1, V2, V3, Z )
% 1.02/1.42 ) ],
% 1.02/1.42 [ =( hAPP( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), Y ), ~(
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice'( X, T, U, W, V0, V1, V2, V3, Z )
% 1.02/1.42 ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Z ), 'c_Collect'( T, X ) ) ) ), ~( hBOOL( hAPP( T, Y ) ) ), ~( hBOOL(
% 1.02/1.42 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.02/1.42 [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( W, V0, V1, T, U )
% 1.02/1.42 ) ), =( hAPP( X, hAPP( Y, V2 ) ), hAPP( W, hAPP( V0, V2 ) ) ) ],
% 1.02/1.42 [ ~( =( hAPP( X, hAPP( Y, Z ) ), hAPP( T, hAPP( U, W ) ) ) ), =( hAPP(
% 1.02/1.42 'c_Fun_Ocomp'( X, Y, V0, V1, V2 ), Z ), hAPP( 'c_Fun_Ocomp'( T, U, V3, V1
% 1.02/1.42 , V4 ), W ) ) ],
% 1.02/1.42 [ =( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 1.02/1.42 , 'tc_bool' ) ), Z ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 1.02/1.42 , 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.02/1.42 Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Y, Z, T ), U, T ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.42 , 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( T, 'tc_bool' ) ), T ), U, T ) ), 'c_Set_Ovimage'( X, Z, U, T )
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Y, 'tc_bool' ) ) ) ) ],
% 1.02/1.42 [ =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , Y ), Z ), T, X, 'tc_fun'( U, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.42 , 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y, T, X,
% 1.02/1.42 'tc_fun'( U, 'tc_bool' ) ) ),
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, T, X, 'tc_fun'(
% 1.02/1.42 U, 'tc_bool' ) ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( X, hAPP( Y, Z ) ) ), ~( hBOOL( hAPP( 'c_Set_Ovimage'( Y,
% 1.02/1.42 X, T, U ), Z ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( 'c_Set_Ovimage'( X, Y, Z, T ), U ) ), ~( hBOOL( hAPP( Y,
% 1.02/1.42 hAPP( X, U ) ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.42 'c_Finite__Set_Olinorder__class_OMin'( Y, X ), Z, X ), ~( hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( X ), Z ), Y ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ =( 'c_Finite__Set_Ofold__image'( X, Y, Z, 'c_Set_Oinsert'( T, U, W ),
% 1.02/1.42 V0, W ), hAPP( hAPP( X, hAPP( Y, T ) ), 'c_Finite__Set_Ofold__image'( X,
% 1.02/1.42 Y, Z, U, V0, W ) ) ), hBOOL( hAPP( hAPP( 'c_in'( W ), T ), U ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( U, W ) ), ~(
% 1.02/1.42 'c_OrderedGroup_Oab__semigroup__mult'( X, V0 ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), T ) ), ~( hBOOL( hAPP( Z, T ) ) ),
% 1.02/1.42 ~( hBOOL( hAPP( Y, T ) ) ) ],
% 1.02/1.42 [ =( 'c_Set_Ovimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ),
% 1.02/1.42 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z, 'tc_bool' ) ) ), ~( hBOOL(
% 1.02/1.42 hAPP( hAPP( 'c_in'( Y ), X ), T ) ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.02/1.42 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), Z ), ~(
% 1.02/1.42 'c_lessequals'( X, Y, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( Z
% 1.02/1.42 , X, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.02/1.42 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.02/1.42 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.02/1.42 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.02/1.42 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.02/1.42 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.02/1.42 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.02/1.42 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.02/1.42 [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z
% 1.02/1.42 , T ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y, U, 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), 'c_lessequals'(
% 1.02/1.42 'c_Set_Oimage'( T, X, Z, U ), 'c_Set_Oimage'( T, Y, Z, U ), 'tc_fun'( U,
% 1.02/1.42 'tc_bool' ) ) ],
% 1.02/1.42 [ =( 'c_Collect'( hAPP( 'c_fequal'( X ), Y ), X ), 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ],
% 1.02/1.42 [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z )
% 1.02/1.42 , 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Fun_Oinj__on'( Z, X, Y, T ) ),
% 1.02/1.42 ~( 'c_Finite__Set_Ofinite'( 'c_Set_Oimage'( Z, X, Y, T ), T ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.42 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.42 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.02/1.42 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), =( X, Y )
% 1.02/1.42 , ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.42 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.42 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.42 , ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.42 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.42 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.02/1.42 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.02/1.42 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.42 'c_Finite__Set_Olinorder__class_OMax'( Z, X ), X ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( X ), Y ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oimage'( X, hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 , Z ), T ), Y, U ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.42 , 'c_Set_Oimage'( X, Z, Y, U ) ), 'c_Set_Oimage'( X, T, Y, U ) ) ) ],
% 1.02/1.42 [ =( 'c_Collect'( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ), 'tc_bool' ), Y ), X ), Y ) ],
% 1.02/1.42 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), 'c_lessequals'(
% 1.02/1.42 Y, 'c_Complete__Lattice_OSup__class_OSup'( Z, X ), X ), ~( hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.02/1.42 [ =( 'c_Fun_Ofcomp'( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W, Z, U, V0 ),
% 1.02/1.42 'c_Fun_Ofcomp'( X, 'c_Fun_Ofcomp'( Y, W, T, U, V0 ), Z, T, V0 ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.42 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.02/1.42 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.02/1.42 'c_lessequals'( Z, Y, X ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.02/1.42 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.02/1.42 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.02/1.42 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), 'c_Set_Oimage'( Y, T,
% 1.02/1.42 U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), 'c_Set_Oimage'( Y, T,
% 1.02/1.42 U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP( 'c_in'( X )
% 1.02/1.42 , 'c_Finite__Set_Olinorder__class_OMin'( Y, X ) ), Y ) ), =( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP( 'c_in'( X )
% 1.02/1.42 , 'c_Finite__Set_Olinorder__class_OMax'( Y, X ) ), Y ) ), =( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.02/1.42 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 1.02/1.42 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y ), ~( hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( Z ), X ), Y ) ) ) ],
% 1.02/1.42 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ),
% 1.02/1.42 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( U, 'tc_bool' ) ), U ), T, U ) ) ) ) ],
% 1.02/1.42 [ =( 'c_Set_Ovimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( Y ), X ), T ) ) ],
% 1.02/1.42 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y, Z, T, 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ),
% 1.02/1.42 'c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1'( Y, Z
% 1.02/1.42 , T, X ) ), Y ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 1.02/1.42 'c_Set_Oinsert'( hAPP( Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.02/1.42 T, 'tc_bool' ) ), T ), X, T ) ) ) ],
% 1.02/1.42 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.02/1.42 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1'(
% 1.02/1.42 Y, X ) ),
% 1.02/1.42 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2'(
% 1.02/1.42 Y, X ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), Y )
% 1.02/1.42 ), ~( 'c_OrderedGroup_Oab__semigroup__mult'( T, U ) ) ],
% 1.02/1.42 [ =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, Y, Z,
% 1.02/1.42 'tc_fun'( T, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.42 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ),
% 1.02/1.42 'c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1'( X, Y
% 1.02/1.42 , Z, T ) ), X ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ),
% 1.02/1.42 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Y ), hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( Z ), X ), Y ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.02/1.42 'c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2'( Y, Z, X ) )
% 1.02/1.42 , Z ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.02/1.42 'c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1'( Y, Z, X ) )
% 1.02/1.42 , Y ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( X ) ), Y ), Y ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( X ) ), Y ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( X ) ), Y ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( X ) ), 'c_Orderings_Obot__class_Obot'( X
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.02/1.42 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.02/1.42 [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.02/1.42 'tc_bool' ) ), Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.02/1.42 ) ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( T, 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( hAPP( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X, T, U, W, V0, V1
% 1.02/1.42 , V2, Z, Y ) ) ],
% 1.02/1.42 [ =( hAPP( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.42 ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( T, X, U, W, V0, V1
% 1.02/1.42 , Z, V2, Y ) ) ],
% 1.02/1.42 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.02/1.42 'c_Collect'( Y, X ) ) ), ~( hBOOL( hAPP( Y, Z ) ) ) ],
% 1.02/1.42 [ 'c_Relation_Ototal__on'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ), Y, X ) ],
% 1.02/1.42 [ =( 'c_Finite__Set_Ofold__image'( X, Y, Z,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), U, T ), Z ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.02/1.42 'c_Set_Oinsert'( Y, Z, X ) ) ) ],
% 1.02/1.42 [ =( 'c_Finite__Set_Ofold'( X, Y, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), Y ) ],
% 1.02/1.42 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.02/1.42 ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ],
% 1.02/1.42 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.02/1.42 ~( 'c_lessequals'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.02/1.42 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.02/1.42 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ],
% 1.02/1.42 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.02/1.42 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ],
% 1.02/1.42 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.02/1.42 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ],
% 1.02/1.42 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.02/1.42 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ],
% 1.02/1.42 [ ~( =( 'c_Collect'( X, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.02/1.42 , 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( X, Z ) ) ) ],
% 1.02/1.42 [ ~( 'c_Wellfounded_Omax__extp'( X, Y, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( 't_a', 'tc_bool' ) ), 't_a' ) ) ],
% 1.02/1.42 [ ~( 'c_Finite__Set_Ofold1Set'( X, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Y, 'tc_bool' ) ), Z, Y ) ) ],
% 1.02/1.42 [ ~( =( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'( X, 'tc_bool' ) ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ), Y ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.02/1.42 ) ) ), Y ), Y ) ],
% 1.02/1.42 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_fun'( Y, 'tc_bool' ) ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ), X ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofinite'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ), X ) ],
% 1.02/1.42 [ =( X, Y ), ~( 'c_Finite__Set_Ofold__graph'( Z, Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), X, T, U ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.42 'tc_bool' ) ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' )
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.02/1.42 ) ) ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.02/1.42 ],
% 1.02/1.42 [ =( 'c_Relation_OImage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.02/1.42 , 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 1.02/1.42 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.02/1.42 ) ), Y, 'tc_fun'( X, 'tc_bool' ) ) ],
% 1.02/1.42 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.02/1.42 'c_Set_Oimage'( Y, Z, T, X ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.02/1.42 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ],
% 1.02/1.42 [ =( 'c_Set_Oimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.02/1.42 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.42 'tc_bool' ) ) ) ],
% 1.02/1.42 [ 'c_Fun_Oinj__on'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.02/1.42 'tc_bool' ) ), Y, Z ) ],
% 1.02/1.42 [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.02/1.42 , 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X, Z ) ],
% 1.02/1.42 [ 'c_Finite__Set_Ofold__graph'( X, Y, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Y, Z, T ) ],
% 1.02/1.42 [ 'c_Nitpick_Ofold__graph_H'( X, Y, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Y, Z, T ) ],
% 1.02/1.42 [ ~( =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ ~( =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.02/1.42 'c_Set_Oimage'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 1.02/1.42 ) ), Z, X ) ) ],
% 1.02/1.42 [ =( 'c_Fun_Ooverride__on'( X, Y, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), X ) ],
% 1.02/1.42 [ =( hAPP( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.42 'tc_fun'( 't_a', 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a',
% 1.02/1.42 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool' ), X ) ), hAPP( 'c_COMBC'( 'c_in'(
% 1.02/1.42 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool' ), Y ) ), 'v_x' )
% 1.02/1.42 , hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( 't_a', 'tc_bool'
% 1.02/1.42 ) ), X ), Y ) ) ) ],
% 1.02/1.42 [ =( hAPP( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.42 'tc_fun'( 't_a', 'tc_bool' ) ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a',
% 1.02/1.42 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool' ), X ) ), hAPP( 'c_COMBC'( 'c_in'(
% 1.02/1.42 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool' ), Y ) ), 'v_x' )
% 1.02/1.42 , hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ), hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( 't_a', 'tc_bool'
% 1.02/1.42 ) ), X ), Y ) ) ) ],
% 1.02/1.42 [ =( hAPP( 'c_Map_Orestrict__map'( X, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( 't_a', 'tc_bool' ) ), 't_a', Y ), 'v_x' ),
% 1.02/1.42 'c_Option_Ooption_ONone'( Y ) ) ],
% 1.02/1.42 [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, 't_a' ), 'v_x' ), hAPP( X, hAPP( Y
% 1.02/1.42 , 'v_x' ) ) ) ],
% 1.02/1.42 [ =( hAPP( 'c_Fun_Oid'( 't_a' ), 'v_x' ), 'v_x' ) ],
% 1.02/1.42 [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, 't_a', Z, T ), 'v_x' ), hAPP( Y, hAPP(
% 1.02/1.42 X, 'v_x' ) ) ) ],
% 1.02/1.42 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ), Y ) ],
% 1.02/1.42 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, Z ), ~(
% 1.02/1.42 'c_Hoare__Mirabelle_Otriple__valid'( 'c_Suc'( X ), Y, Z ) ) ],
% 1.02/1.42 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~( hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y ), Z ) ) ),
% 1.02/1.42 hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.02/1.42 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1'( T, X ) ), T ) ), ~(
% 1.02/1.42 'c_Hoare__Mirabelle_Ohoare__valids'( T, Z, 't_a' ) ) ],
% 1.02/1.42 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~( hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y ), Z ) ) ), ~(
% 1.02/1.42 'c_Hoare__Mirabelle_Otriple__valid'( 'c_Suc'( X ),
% 1.02/1.42 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1'( X, Z ), 't_a' ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ 'c_Hoare__Mirabelle_Ohoare__valids'( X, Y, 't_a' ),
% 1.02/1.42 'c_Hoare__Mirabelle_Otriple__valid'(
% 1.02/1.42 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__2'( X, Y ), Z, 't_a' ),
% 1.02/1.42 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Z
% 1.02/1.42 ), X ) ) ) ],
% 1.02/1.42 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~( hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y ), Z ) ) ), ~(
% 1.02/1.42 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 1.02/1.42 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1'( T, X ), 't_a' ) ), ~(
% 1.02/1.42 'c_Hoare__Mirabelle_Ohoare__valids'( T, Z, 't_a' ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.02/1.42 'c_ATP__Linkup_Osko__Set__Xex__in__conv__1__1'( Y, X ) ), Y ) ), =( Y,
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.02/1.42 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.02/1.42 hBOOL( hAPP( hAPP( 'c_in'( Y ),
% 1.02/1.42 'c_ATP__Linkup_Osko__Set__Xall__not__in__conv__1__1'( X, Y ) ), X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.42 'c_in'( X ), Y ), T ) ) ), ~( =( hAPP( hAPP(
% 1.02/1.42 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.42 , T ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.02/1.42 ) ],
% 1.02/1.42 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.02/1.42 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y, Z, T, 'tc_fun'(
% 1.02/1.42 X, 'tc_bool' ) ) ) ), =( hAPP( Z, U ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), U ), Y )
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ ~( =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, Y, Z,
% 1.02/1.42 'tc_fun'( T, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.42 'tc_bool' ) ) ) ), =( hAPP( Y, U ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( T, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), X )
% 1.02/1.42 ) ) ],
% 1.02/1.42 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.02/1.42 hBOOL( hAPP( hAPP( 'c_in'( Y ),
% 1.02/1.42 'c_ATP__Linkup_Osko__Set__Xequals0I__1__1'( X, Y ) ), X ) ) ],
% 1.02/1.42 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), 'c_Set_Oinsert'( Y
% 1.02/1.42 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), Y )
% 1.02/1.42 ) ],
% 1.02/1.42 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 1.02/1.42 'c_Complete__Lattice_OSup__class_OSup'( 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ), X ), 'c_Orderings_Obot__class_Obot'( X ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~( hBOOL( hAPP(
% 1.02/1.42 hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y ), Z ) ) ),
% 1.02/1.42 hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.02/1.42 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1'( X, Z ) ), Z ) ) ]
% 1.02/1.42 ,
% 1.02/1.42 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.02/1.42 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.02/1.42 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.42 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.02/1.42 [ =( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' )
% 1.02/1.42 ), 'v_x' ), hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' ) ) ) ) ],
% 1.02/1.42 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.02/1.42 ) ), Y ) ) ) ],
% 1.02/1.42 [ ~( 'class_Orderings_Obot'( X ) ), =( hAPP(
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 1.02/1.42 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.02/1.42 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( Z, Y ) ) )
% 1.02/1.42 ],
% 1.02/1.42 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), X ) ) )
% 1.02/1.43 ],
% 1.02/1.43 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.02/1.43 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.02/1.43 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.02/1.43 'v_xa' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.02/1.43 'tc_Hoare__Mirabelle_Otriple'( 't_a' ), 'tc_bool' ) ) ) ) ],
% 1.02/1.43 [ ~( 'c_Hoare__Mirabelle_Otriple__valid'( 'v_x', 'v_xa', 't_a' ) ) ]
% 1.02/1.43 ,
% 1.02/1.43 [ 'c_Hoare__Mirabelle_Otriple__valid'( 'v_x', X, 't_a' ), ~( hBOOL( hAPP(
% 1.02/1.43 hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), X ), 'v_Ga' ) ) )
% 1.02/1.43 ],
% 1.02/1.43 [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.43 'class_Complete__Lattice_Ocomplete__lattice'( Y ) ) ],
% 1.02/1.43 [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.43 'class_Lattices_Olattice'( Y ) ) ],
% 1.02/1.43 [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.43 'class_Lattices_Olattice'( Y ) ) ],
% 1.02/1.43 [ 'class_Lattices_Odistrib__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.43 'class_Lattices_Odistrib__lattice'( Y ) ) ],
% 1.02/1.43 [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.43 'class_Lattices_Obounded__lattice'( Y ) ) ],
% 1.02/1.43 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.43 'class_Finite__Set_Ofinite_Ofinite'( Y ) ), ~(
% 1.02/1.43 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ],
% 1.02/1.43 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.43 'class_Orderings_Opreorder'( Y ) ) ],
% 1.02/1.43 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.43 'class_Lattices_Olattice'( Y ) ) ],
% 1.02/1.43 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.43 'class_Orderings_Oorder'( Y ) ) ],
% 1.02/1.43 [ 'class_Orderings_Otop'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Otop'(
% 1.02/1.43 Y ) ) ],
% 1.02/1.43 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 1.02/1.43 Y ) ) ],
% 1.02/1.43 [ 'class_HOL_Ominus'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Ominus'( Y ) ) ]
% 1.02/1.43 ,
% 1.02/1.43 [ 'class_HOL_Oord'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Oord'( Y ) ) ]
% 1.02/1.43 ,
% 1.02/1.43 [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ],
% 1.02/1.43 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 1.02/1.43 [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ],
% 1.02/1.43 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.02/1.43 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.02/1.43 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.02/1.43 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.02/1.43 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.02/1.43 [ 'class_HOL_Ominus'( 'tc_nat' ) ],
% 1.02/1.43 [ 'class_HOL_Oord'( 'tc_nat' ) ],
% 1.02/1.43 [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_bool' ) ],
% 1.02/1.43 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 1.02/1.43 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 1.02/1.43 [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ],
% 1.02/1.43 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 1.02/1.43 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_bool' ) ],
% 1.02/1.43 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.02/1.43 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.02/1.43 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.02/1.43 [ 'class_Orderings_Otop'( 'tc_bool' ) ],
% 1.02/1.43 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.02/1.43 [ 'class_HOL_Ominus'( 'tc_bool' ) ],
% 1.02/1.43 [ 'class_HOL_Oord'( 'tc_bool' ) ],
% 1.02/1.43 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_Option_Ooption'( X ) ), ~(
% 1.02/1.43 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ],
% 1.02/1.43 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 1.02/1.43 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 1.02/1.43 ] .
% 1.02/1.43
% 1.02/1.43
% 1.02/1.43 percentage equality = 0.279373, percentage horn = 0.891344
% 1.02/1.43 This is a problem with some equality
% 1.02/1.43
% 1.02/1.43
% 1.02/1.43
% 1.02/1.43 Options Used:
% 1.02/1.43
% 1.02/1.43 useres = 1
% 1.02/1.43 useparamod = 1
% 1.02/1.43 useeqrefl = 1
% 1.02/1.43 useeqfact = 1
% 1.02/1.43 usefactor = 1
% 1.02/1.43 usesimpsplitting = 0
% 1.02/1.43 usesimpdemod = 5
% 1.02/1.43 usesimpres = 3
% 1.02/1.43
% 1.02/1.43 resimpinuse = 1000
% 1.02/1.43 resimpclauses = 20000
% 1.02/1.43 substype = eqrewr
% 1.02/1.43 backwardsubs = 1
% 1.02/1.43 selectoldest = 5
% 1.02/1.43
% 1.02/1.43 litorderings [0] = split
% 1.02/1.43 litorderings [1] = extend the termordering, first sorting on arguments
% 1.02/1.43
% 1.02/1.43 termordering = kbo
% 1.02/1.43
% 1.02/1.43 litapriori = 0
% 1.02/1.43 termapriori = 1
% 1.02/1.43 litaposteriori = 0
% 1.02/1.43 termaposteriori = 0
% 1.02/1.43 demodaposteriori = 0
% 1.02/1.43 ordereqreflfact = 0
% 1.02/1.43
% 1.02/1.43 litselect = negord
% 1.02/1.43
% 1.02/1.43 maxweight = 15
% 1.02/1.43 maxdepth = 30000
% 1.02/1.43 maxlength = 115
% 1.02/1.43 maxnrvars = 195
% 1.02/1.43 excuselevel = 1
% 1.02/1.43 increasemaxweight = 1
% 1.02/1.43
% 1.02/1.43 maxselected = 10000000
% 1.02/1.43 maxnrclauses = 10000000
% 1.02/1.43
% 1.02/1.43 showgenerated = 0
% 1.02/1.43 showkept = 0
% 1.02/1.43 showselected = 0
% 1.02/1.43 showdeleted = 0
% 1.02/1.43 showresimp = 1
% 1.02/1.43 showstatus = 2000
% 1.02/1.43
% 1.02/1.43 prologoutput = 1
% 1.02/1.43 nrgoals = 5000000
% 1.02/1.43 totalproof = 1
% 1.02/1.43
% 1.02/1.43 Symbols occurring in the translation:
% 1.02/1.43
% 1.02/1.43 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.02/1.43 . [1, 2] (w:1, o:112, a:1, s:1, b:0),
% 1.02/1.43 ! [4, 1] (w:0, o:78, a:1, s:1, b:0),
% 1.02/1.43 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.43 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.43 'c_Set_Oimage' [43, 4] (w:1, o:165, a:1, s:1, b:0),
% 1.02/1.43 'tc_bool' [45, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.02/1.43 'tc_fun' [46, 2] (w:1, o:137, a:1, s:1, b:0),
% 1.02/1.43 'c_lessequals' [47, 3] (w:1, o:153, a:1, s:1, b:0),
% 1.02/1.43 'c_Orderings_Otop__class_Otop' [48, 1] (w:1, o:83, a:1, s:1, b:0),
% 1.02/1.43 'c_Fun_Oinj__on' [49, 4] (w:1, o:166, a:1, s:1, b:0),
% 1.02/1.43 'c_Set_Oinsert' [51, 3] (w:1, o:155, a:1, s:1, b:0),
% 1.02/1.43 'class_Complete__Lattice_Ocomplete__lattice' [52, 1] (w:1, o:84, a:1
% 1.02/1.43 , s:1, b:0),
% 1.02/1.43 hAPP [55, 2] (w:1, o:138, a:1, s:1, b:0),
% 1.02/1.43 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR' [56, 4] (w:1
% 1.02/1.43 , o:167, a:1, s:1, b:0),
% 1.02/1.43 'c_in' [57, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.02/1.43 hBOOL [58, 1] (w:1, o:86, a:1, s:1, b:0),
% 1.02/1.43 'c_HOL_Ominus__class_Ominus' [60, 3] (w:1, o:156, a:1, s:1, b:0),
% 1.02/1.43 'c_Finite__Set_Ofold1Set' [62, 4] (w:1, o:168, a:1, s:1, b:0),
% 1.02/1.43 'c_Finite__Set_Ofold__graph' [63, 6] (w:1, o:179, a:1, s:1, b:0),
% 1.02/1.43 'c_Complete__Lattice_Ocomplete__lattice' [72, 9] (w:1, o:182, a:1, s:
% 1.02/1.43 1, b:0),
% 1.02/1.43 'c_Orderings_Obot__class_Obot' [73, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.02/1.43 'c_HOL_Oord__class_Oless' [74, 3] (w:1, o:157, a:1, s:1, b:0),
% 1.02/1.43 'c_Finite__Set_Ofold__image' [80, 6] (w:1, o:180, a:1, s:1, b:0),
% 1.02/1.43 'c_Fun_Ocomp' [81, 5] (w:1, o:175, a:1, s:1, b:0),
% 1.02/1.43 'c_Finite__Set_Ofinite' [82, 2] (w:1, o:139, a:1, s:1, b:0),
% 1.02/1.43 'c_OrderedGroup_Oab__semigroup__mult' [83, 2] (w:1, o:140, a:1, s:1
% 1.02/1.43 , b:0),
% 1.02/1.43 'class_Lattices_Oupper__semilattice' [84, 1] (w:1, o:88, a:1, s:1, b:
% 1.02/1.43 0),
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup' [85, 1] (w:1, o:89, a:1
% 1.02/1.43 , s:1, b:0),
% 1.02/1.43 'c_Finite__Set_Ofold' [86, 5] (w:1, o:176, a:1, s:1, b:0),
% 1.02/1.43 'c_Set_Ovimage' [88, 4] (w:1, o:169, a:1, s:1, b:0),
% 1.02/1.43 'c_Collect' [90, 2] (w:1, o:141, a:1, s:1, b:0),
% 1.02/1.43 'c_Complete__Lattice_OSup__class_OSup' [91, 2] (w:1, o:142, a:1, s:1
% 1.02/1.43 , b:0),
% 1.02/1.43 'class_Lattices_Obounded__lattice' [92, 1] (w:1, o:90, a:1, s:1, b:0)
% 1.02/1.43 ,
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf' [93, 1] (w:1, o:91, a:1
% 1.02/1.43 , s:1, b:0),
% 1.02/1.43
% 1.02/1.43 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1'
% 1.02/1.43 [95, 2] (w:1, o:143, a:1, s:1, b:0),
% 1.02/1.43
% 1.02/1.43 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2'
% 1.02/1.43 [96, 2] (w:1, o:144, a:1, s:1, b:0),
% 1.02/1.43 'c_COMBK' [99, 3] (w:1, o:158, a:1, s:1, b:0),
% 1.02/1.43 't_a' [100, 0] (w:1, o:51, a:1, s:1, b:0),
% 1.02/1.43 'v_x' [101, 0] (w:1, o:52, a:1, s:1, b:0),
% 1.02/1.43 'c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1' [103, 4
% 1.02/1.43 ] (w:1, o:171, a:1, s:1, b:0),
% 1.02/1.43 'c_Relation_OImage' [107, 4] (w:1, o:164, a:1, s:1, b:0),
% 1.02/1.43 'c_Map_Orestrict__map' [109, 4] (w:1, o:172, a:1, s:1, b:0),
% 1.02/1.43 'c_Option_Ooption_ONone' [110, 1] (w:1, o:92, a:1, s:1, b:0),
% 1.02/1.43 'c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1' [111, 3]
% 1.02/1.43 (w:1, o:159, a:1, s:1, b:0),
% 1.02/1.43 'c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2' [112, 3]
% 1.02/1.43 (w:1, o:160, a:1, s:1, b:0),
% 1.02/1.43 'c_Suc' [114, 1] (w:1, o:93, a:1, s:1, b:0),
% 1.02/1.43 'class_Lattices_Olattice' [117, 1] (w:1, o:94, a:1, s:1, b:0),
% 1.02/1.43 'class_Lattices_Odistrib__lattice' [118, 1] (w:1, o:95, a:1, s:1, b:0
% 1.02/1.43 ),
% 1.02/1.43 'c_Fun_Oid' [119, 1] (w:1, o:96, a:1, s:1, b:0),
% 1.02/1.43 'class_Orderings_Opreorder' [120, 1] (w:1, o:98, a:1, s:1, b:0),
% 1.02/1.43 'class_Orderings_Oorder' [121, 1] (w:1, o:97, a:1, s:1, b:0),
% 1.02/1.43 'c_COMBC' [122, 4] (w:1, o:173, a:1, s:1, b:0),
% 1.02/1.43 'class_Orderings_Olinorder' [124, 1] (w:1, o:99, a:1, s:1, b:0),
% 1.02/1.43 'class_HOL_Oord' [125, 1] (w:1, o:100, a:1, s:1, b:0),
% 1.02/1.43 'class_OrderedGroup_Oab__group__add' [126, 1] (w:1, o:101, a:1, s:1
% 1.02/1.43 , b:0),
% 1.02/1.43 'c_Finite__Set_Olinorder__class_OMax' [130, 2] (w:1, o:145, a:1, s:1
% 1.02/1.43 , b:0),
% 1.02/1.43 'class_Lattices_Olower__semilattice' [132, 1] (w:1, o:102, a:1, s:1
% 1.02/1.43 , b:0),
% 1.02/1.43 'c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1' [133, 4
% 1.02/1.43 ] (w:1, o:170, a:1, s:1, b:0),
% 1.02/1.43 'c_Finite__Set_Olinorder__class_OMin' [134, 2] (w:1, o:146, a:1, s:1
% 1.02/1.43 , b:0),
% 1.02/1.43 'class_Orderings_Otop' [136, 1] (w:1, o:103, a:1, s:1, b:0),
% 1.02/1.43 'class_Ring__and__Field_Oordered__idom' [138, 1] (w:1, o:104, a:1, s:
% 1.02/1.43 1, b:0),
% 1.02/1.43 'c_Hoare__Mirabelle_Ohoare__derivs' [140, 3] (w:1, o:161, a:1, s:1
% 1.02/1.43 , b:0),
% 1.02/1.43 'c_Fun_Ofcomp' [142, 5] (w:1, o:177, a:1, s:1, b:0),
% 1.02/1.43 'class_HOL_Ominus' [144, 1] (w:1, o:105, a:1, s:1, b:0),
% 1.02/1.43 'c_fequal' [145, 1] (w:1, o:106, a:1, s:1, b:0),
% 1.02/1.43 'class_Finite__Set_Ofinite_Ofinite' [147, 1] (w:1, o:107, a:1, s:1
% 1.02/1.43 , b:0),
% 1.02/1.43 'c_Nitpick_Ofold__graph_H' [148, 6] (w:1, o:181, a:1, s:1, b:0),
% 1.02/1.43 'c_Wellfounded_Omax__extp' [151, 4] (w:1, o:174, a:1, s:1, b:0),
% 1.02/1.43 'c_Fun_Ooverride__on' [153, 5] (w:1, o:178, a:1, s:1, b:0),
% 1.02/1.43 'class_OrderedGroup_Opordered__ab__group__add' [161, 1] (w:1, o:108
% 1.02/1.43 , a:1, s:1, b:0),
% 1.02/1.43 'class_Orderings_Obot' [162, 1] (w:1, o:109, a:1, s:1, b:0),
% 1.02/1.43 'c_Relation_Ototal__on' [163, 3] (w:1, o:154, a:1, s:1, b:0),
% 1.02/1.43 'tc_Hoare__Mirabelle_Otriple' [164, 1] (w:1, o:110, a:1, s:1, b:0),
% 1.02/1.43 'c_Hoare__Mirabelle_Otriple__valid' [165, 3] (w:1, o:162, a:1, s:1
% 1.02/1.43 , b:0),
% 1.02/1.43 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1' [167, 2] (w:1, o:
% 1.02/1.43 147, a:1, s:1, b:0),
% 1.02/1.43 'c_Hoare__Mirabelle_Ohoare__valids' [168, 3] (w:1, o:163, a:1, s:1
% 1.02/1.43 , b:0),
% 1.02/1.43 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1' [169, 2] (w:1, o:
% 1.02/1.43 148, a:1, s:1, b:0),
% 1.02/1.43 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__2' [170, 2] (w:1, o:
% 1.02/1.43 149, a:1, s:1, b:0),
% 1.02/1.43 'c_ATP__Linkup_Osko__Set__Xex__in__conv__1__1' [172, 2] (w:1, o:150
% 1.02/1.43 , a:1, s:1, b:0),
% 1.02/1.43 'c_ATP__Linkup_Osko__Set__Xall__not__in__conv__1__1' [173, 2] (w:1
% 1.02/1.43 , o:151, a:1, s:1, b:0),
% 1.02/1.43 'c_ATP__Linkup_Osko__Set__Xequals0I__1__1' [174, 2] (w:1, o:152, a:1
% 1.02/1.43 , s:1, b:0),
% 1.02/1.43 'v_xa' [175, 0] (w:1, o:73, a:1, s:1, b:0),
% 1.02/1.43 'v_Ga' [177, 0] (w:1, o:74, a:1, s:1, b:0),
% 1.02/1.43 'tc_nat' [180, 0] (w:1, o:77, a:1, s:1, b:0),
% 1.02/1.43 'tc_Option_Ooption' [181, 1] (w:1, o:111, a:1, s:1, b:0).
% 1.02/1.43
% 1.02/1.43
% 1.02/1.43 Starting Search:
% 1.02/1.43
% 1.02/1.43
% 1.02/1.43 Bliksems!, er is een bewijs:
% 1.02/1.43 % SZS status Unsatisfiable
% 1.02/1.43 % SZS output start Refutation
% 1.02/1.43
% 1.02/1.43 clause( 470, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.43 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.02/1.43 .
% 1.02/1.43 clause( 474, [] )
% 1.02/1.43 .
% 1.02/1.43
% 1.02/1.43
% 1.02/1.43 % SZS output end Refutation
% 1.02/1.43 found a proof!
% 1.02/1.43
% 1.02/1.43 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.02/1.43
% 1.02/1.43 initialclauses(
% 1.02/1.43 [ clause( 476, [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ),
% 1.02/1.43 'c_Set_Oimage'( X, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 1.02/1.43 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'(
% 1.02/1.43 X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ) ]
% 1.02/1.43 )
% 1.02/1.43 , clause( 477, [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X,
% 1.02/1.43 'c_Set_Oinsert'( U, Y, Z ), Z, T ) ) ] )
% 1.02/1.43 , clause( 478, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.02/1.43 'c_lessequals'( hAPP( Y, Z ),
% 1.02/1.43 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( T, Y, U, X ), X )
% 1.02/1.43 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ) ] )
% 1.02/1.43 , clause( 479, [ 'c_lessequals'( hAPP( X, Y ),
% 1.02/1.43 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, X, T, 'tc_fun'(
% 1.02/1.43 U, 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.43 'c_in'( T ), Y ), Z ) ) ) ] )
% 1.02/1.43 , clause( 480, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z
% 1.02/1.43 ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, T,
% 1.02/1.43 'tc_fun'( Z, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T )
% 1.02/1.43 ) ) ] )
% 1.02/1.43 , clause( 481, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.43 'c_lessequals'( 'c_Set_Oinsert'( T, X, Z ), Y, 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.43 ) ] )
% 1.02/1.43 , clause( 482, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.02/1.43 , 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ]
% 1.02/1.43 )
% 1.02/1.43 , clause( 483, [ 'c_Finite__Set_Ofold1Set'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 1.02/1.43 U, T ), hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), Z ) ), ~(
% 1.02/1.43 'c_Finite__Set_Ofold__graph'( X, Y, Z, U, T, T ) ) ] )
% 1.02/1.43 , clause( 484, [ =( hAPP( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.02/1.43 'tc_bool' ) ) ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( T, X,
% 1.02/1.43 U, W, V0, V1, V2, Z, Y ) ) ] )
% 1.02/1.43 , clause( 485, [ =( hAPP( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.02/1.43 'tc_bool' ) ) ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X, T,
% 1.02/1.43 U, W, V0, V1, Z, V2, Y ) ) ] )
% 1.02/1.43 , clause( 486, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X
% 1.02/1.43 , 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.43 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool'
% 1.02/1.43 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), X ) ) ), hBOOL( hAPP( hAPP(
% 1.02/1.43 'c_in'( Z ), Y ), T ) ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'(
% 1.02/1.43 Y, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 487, [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 1.02/1.43 'tc_fun'( T, 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) )
% 1.02/1.43 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.43 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.43 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool'
% 1.02/1.43 ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), Z ) ) ] )
% 1.02/1.43 , clause( 488, [ =( 'c_Finite__Set_Ofold__image'( X, Y, Z, 'c_Set_Oimage'(
% 1.02/1.43 T, U, W, V0 ), V1, V0 ), 'c_Finite__Set_Ofold__image'( X, 'c_Fun_Ocomp'(
% 1.02/1.43 Y, T, V0, V1, W ), Z, U, V1, W ) ), ~( 'c_Fun_Oinj__on'( T, U, W, V0 ) )
% 1.02/1.43 , ~( 'c_Finite__Set_Ofinite'( U, W ) ), ~(
% 1.02/1.43 'c_OrderedGroup_Oab__semigroup__mult'( X, V1 ) ) ] )
% 1.02/1.43 , clause( 489, [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.43 Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z ) )
% 1.02/1.43 ] )
% 1.02/1.43 , clause( 490, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.43 'c_lessequals'( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.43 X ), Y ), Z ), 'c_Finite__Set_Ofold'(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z, T, X, X ), X ), ~(
% 1.02/1.43 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( 'c_Finite__Set_Ofinite'(
% 1.02/1.43 T, X ) ) ] )
% 1.02/1.43 , clause( 491, [ 'c_Fun_Oinj__on'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.02/1.43 'tc_fun'( T, 'tc_bool' ) ), T, U ), ~( 'c_Fun_Oinj__on'( X, Y, T, U ) ) ]
% 1.02/1.43 )
% 1.02/1.43 , clause( 492, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , 'c_Set_Oinsert'( Y, Z, X ) ), T ), 'c_Set_Oinsert'( Y, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Z ), T ), X ) ) ] )
% 1.02/1.43 , clause( 493, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), 'c_Set_Oinsert'( Z, T, X ) ), 'c_Set_Oinsert'( Z, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), T ), X ) ) ] )
% 1.02/1.43 , clause( 494, [ =( 'c_Set_Ovimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.02/1.43 , 'tc_fun'( T, 'tc_bool' ) ), U, T ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.43 'c_Set_Ovimage'( X, Y, U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U
% 1.02/1.43 , 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 495, [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 1.02/1.43 'tc_fun'( T, 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) )
% 1.02/1.43 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.43 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.43 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool'
% 1.02/1.43 ) ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) )
% 1.02/1.43 ] )
% 1.02/1.43 , clause( 496, [ 'c_lessequals'( 'c_Set_Oimage'( X, 'c_Set_Ovimage'( X, Y,
% 1.02/1.43 Z, T ), Z, T ), Y, 'tc_fun'( T, 'tc_bool' ) ) ] )
% 1.02/1.43 , clause( 497, [ =( 'c_Set_Ovimage'( X, 'c_Set_Oimage'( X, Y, Z, T ), Z, T
% 1.02/1.43 ), Y ), ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'(
% 1.02/1.43 Z, 'tc_bool' ) ), Z, T ) ) ] )
% 1.02/1.43 , clause( 498, [ =( 'c_Collect'( X, Y ), X ) ] )
% 1.02/1.43 , clause( 499, [ =( X, Y ), ~( 'c_Finite__Set_Ofold1Set'( Z,
% 1.02/1.43 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.43 'tc_bool' ) ), T ), Y, T ) ) ] )
% 1.02/1.43 , clause( 500, [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Otop__class_Otop'(
% 1.02/1.43 'tc_fun'( Y, 'tc_bool' ) ), Z, Y ), 'c_Orderings_Otop__class_Otop'(
% 1.02/1.43 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 501, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.02/1.43 =( 'c_Complete__Lattice_OSup__class_OSup'( 'c_Set_Oinsert'( Y, Z, X ), X
% 1.02/1.43 ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ),
% 1.02/1.43 'c_Complete__Lattice_OSup__class_OSup'( Z, X ) ) ) ] )
% 1.02/1.43 , clause( 502, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ),
% 1.02/1.43 'c_Orderings_Otop__class_Otop'( X ) ), 'c_Orderings_Otop__class_Otop'( X
% 1.02/1.43 ) ) ] )
% 1.02/1.43 , clause( 503, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.02/1.43 'c_Orderings_Otop__class_Otop'( X ) ), Y ),
% 1.02/1.43 'c_Orderings_Otop__class_Otop'( X ) ) ] )
% 1.02/1.43 , clause( 504, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ), Y ),
% 1.02/1.43 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 505, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.02/1.43 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 506, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y, Z
% 1.02/1.43 , T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.43 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ),
% 1.02/1.43 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.43 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 507, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y, Z
% 1.02/1.43 , T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.43 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.43 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.02/1.43 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 508, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.02/1.43 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y
% 1.02/1.43 , 'tc_bool' ) ), Y ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ] )
% 1.02/1.43 , clause( 509, [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.43 Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z ) )
% 1.02/1.43 , ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ] )
% 1.02/1.43 , clause( 510, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , 'c_Set_Oinsert'( Y, Z, X ) ), 'c_Set_Oinsert'( Y, T, X ) ),
% 1.02/1.43 'c_Set_Oinsert'( Y, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Z ), T ), X ) ) ] )
% 1.02/1.43 , clause( 511, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.02/1.43 'c_Set_Oinsert'( X, Y, Z ) ) ] )
% 1.02/1.43 , clause( 512, [ 'c_Finite__Set_Ofinite'( hAPP( X, Y ), Z ), ~( hBOOL( hAPP(
% 1.02/1.43 hAPP( 'c_in'( T ), Y ), U ) ) ), ~( 'c_Finite__Set_Ofinite'(
% 1.02/1.43 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( U, X, T, 'tc_fun'(
% 1.02/1.43 Z, 'tc_bool' ) ), Z ) ), ~( 'c_Finite__Set_Ofinite'( U, T ) ) ] )
% 1.02/1.43 , clause( 513, [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 1.02/1.43 'c_Set_Oinsert'( Z, X, T ), Y ) ) ) ] )
% 1.02/1.43 , clause( 514, [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U,
% 1.02/1.43 Z, T ) ) ), ~( 'c_Fun_Oinj__on'( X, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.43 , Y ), U ), Z, T ) ), =( Y, U ) ] )
% 1.02/1.43 , clause( 515, [ =( X, 'c_Set_Oinsert'(
% 1.02/1.43 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1'(
% 1.02/1.43 X, Y ),
% 1.02/1.43 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2'(
% 1.02/1.43 X, Y ), Y ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.02/1.43 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 516, [ 'c_lessequals'( hAPP( X, Y ), Z, 'tc_fun'( T, 'tc_bool' )
% 1.02/1.43 ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Y ), W ) ) ), ~( 'c_lessequals'(
% 1.02/1.43 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( W, X, U, 'tc_fun'(
% 1.02/1.43 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 517, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, X, Z ), 'tc_fun'( Z
% 1.02/1.43 , 'tc_bool' ) ) ] )
% 1.02/1.43 , clause( 518, [ =( hAPP( 'c_Fun_Ocomp'( 'c_COMBK'( X, Y, Z ), T, Z, Y,
% 1.02/1.43 't_a' ), 'v_x' ), X ) ] )
% 1.02/1.43 , clause( 519, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.02/1.43 'c_Finite__Set_Ofinite'( 'c_Set_Oinsert'( Z, X, Y ), Y ) ) ] )
% 1.02/1.43 , clause( 520, [ 'c_Finite__Set_Ofinite'( 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.02/1.43 ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ] )
% 1.02/1.43 , clause( 521, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , hAPP( Y, Z ) ), 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.43 T, Y, U, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.02/1.43 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( T, Y, U, 'tc_fun'(
% 1.02/1.43 X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ) ] )
% 1.02/1.43 , clause( 522, [ ~( =( hAPP( X,
% 1.02/1.43 'c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1'( Y, X
% 1.02/1.43 , Z, T ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) )
% 1.02/1.43 ), =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y, X, Z,
% 1.02/1.43 'tc_fun'( T, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.43 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 523, [ 'c_Finite__Set_Ofold__graph'( X, Y, Z, hAPP( hAPP( X, T )
% 1.02/1.43 , U ), W, V0 ), ~( hBOOL( hAPP( hAPP( 'c_in'( W ), T ), Z ) ) ), ~(
% 1.02/1.43 'c_Finite__Set_Ofold__graph'( X, Y, 'c_HOL_Ominus__class_Ominus'( Z,
% 1.02/1.43 'c_Set_Oinsert'( T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( W,
% 1.02/1.43 'tc_bool' ) ), W ), 'tc_fun'( W, 'tc_bool' ) ), U, W, V0 ) ) ] )
% 1.02/1.43 , clause( 524, [ =( 'c_Set_Oimage'( X, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.43 , Z ), T ), Y, U ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.43 , 'c_Set_Oimage'( X, Z, Y, U ) ), 'c_Set_Oimage'( X, T, Y, U ) ) ), ~(
% 1.02/1.43 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.02/1.43 'tc_bool' ) ), Y, U ) ) ] )
% 1.02/1.43 , clause( 525, [ =( hAPP( X, 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( Z,
% 1.02/1.43 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T ) ),
% 1.02/1.43 hAPP( hAPP( U, Y ), Z ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W
% 1.02/1.43 , X, V0, V1, V2, U, V3, V4, T ) ) ] )
% 1.02/1.43 , clause( 526, [ =( hAPP( X, 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( Z,
% 1.02/1.43 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T ) ),
% 1.02/1.43 hAPP( hAPP( U, Y ), Z ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X
% 1.02/1.43 , W, V0, V1, U, V2, V3, V4, T ) ) ] )
% 1.02/1.43 , clause( 527, [ 'c_lessequals'( 'c_Set_Oimage'( X, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.43 , Z ), T ), Y, U ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.43 , 'c_Set_Oimage'( X, Z, Y, U ) ), 'c_Set_Oimage'( X, T, Y, U ) ),
% 1.02/1.43 'tc_fun'( U, 'tc_bool' ) ) ] )
% 1.02/1.43 , clause( 528, [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), ~(
% 1.02/1.43 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.02/1.43 , clause( 529, [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), ~(
% 1.02/1.43 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.02/1.43 , clause( 530, [ 'c_lessequals'( 'c_Relation_OImage'( X, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.43 , Z ), T ), Y, U ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.43 , 'c_Relation_OImage'( X, Z, Y, U ) ), 'c_Relation_OImage'( X, T, Y, U )
% 1.02/1.43 ), 'tc_fun'( U, 'tc_bool' ) ) ] )
% 1.02/1.43 , clause( 531, [ ~( =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.02/1.43 'tc_bool' ) ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.43 X, 'tc_bool' ) ), Z ), T ) ) ) ), 'c_lessequals'( T, Y, 'tc_fun'( X,
% 1.02/1.43 'tc_bool' ) ) ] )
% 1.02/1.43 , clause( 532, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.02/1.43 'tc_bool' ) ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.43 X, 'tc_bool' ) ), Z ), T ) ) ), ~( 'c_lessequals'( T, Y, 'tc_fun'( X,
% 1.02/1.43 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 533, [ =( hAPP( 'c_Map_Orestrict__map'( X, Y, Z, T ), U ),
% 1.02/1.43 'c_Option_Ooption_ONone'( T ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), Y )
% 1.02/1.43 ) ] )
% 1.02/1.43 , clause( 534, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.02/1.43 , =( 'c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1'( Y, Z, X
% 1.02/1.43 ), 'c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2'( Y, Z, X
% 1.02/1.43 ) ) ] )
% 1.02/1.43 , clause( 535, [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W ), hAPP( X,
% 1.02/1.43 hAPP( Y, W ) ) ) ] )
% 1.02/1.43 , clause( 536, [ =( hAPP( X, hAPP( Y, Z ) ), hAPP( 'c_Fun_Ocomp'( X, Y, T,
% 1.02/1.43 U, W ), Z ) ) ] )
% 1.02/1.43 , clause( 537, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.02/1.43 hAPP( 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) ) ),
% 1.02/1.43 ~( 'c_Fun_Oinj__on'( U, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.02/1.43 'tc_bool' ) ), X, T ) ) ] )
% 1.02/1.43 , clause( 538, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ),
% 1.02/1.43 'c_Set_Oimage'( Y, T, U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z )
% 1.02/1.43 , T ) ) ), ~( 'c_Fun_Oinj__on'( Y, 'c_Orderings_Otop__class_Otop'(
% 1.02/1.43 'tc_fun'( U, 'tc_bool' ) ), U, X ) ) ] )
% 1.02/1.43 , clause( 539, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 1.02/1.43 , clause( 540, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 1.02/1.43 , clause( 541, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP(
% 1.02/1.43 hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ) ), ~(
% 1.02/1.43 'c_OrderedGroup_Oab__semigroup__mult'( X, U ) ) ] )
% 1.02/1.43 , clause( 542, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 1.02/1.43 hAPP( X, Z ), hAPP( hAPP( X, Y ), T ) ) ), ~(
% 1.02/1.43 'c_OrderedGroup_Oab__semigroup__mult'( X, U ) ) ] )
% 1.02/1.43 , clause( 543, [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.02/1.43 'c_OrderedGroup_Oab__semigroup__mult'( X, T ) ) ] )
% 1.02/1.43 , clause( 544, [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( 'c_Fun_Oinj__on'(
% 1.02/1.43 X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( T, 'tc_bool' ) ), T, U ) ),
% 1.02/1.43 =( Y, Z ) ] )
% 1.02/1.43 , clause( 545, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL(
% 1.02/1.43 hAPP( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.43 T, 'tc_bool' ) ), Z ), X ), Y ) ) ) ] )
% 1.02/1.43 , clause( 546, [ hBOOL( hAPP( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), Z ), T ) ), ~( hBOOL( hAPP( Z, T ) ) ) ] )
% 1.02/1.43 , clause( 547, [ hBOOL( hAPP( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), Z ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ] )
% 1.02/1.43 , clause( 548, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.43 'c_lessequals'( 'c_Set_Oimage'( T, X, Z, U ), 'c_Set_Oimage'( T, Y, Z, U
% 1.02/1.43 ), 'tc_fun'( U, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( T,
% 1.02/1.43 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z, 'tc_bool' ) ), Z, U ) ) ] )
% 1.02/1.43 , clause( 549, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.02/1.43 , 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ), ~(
% 1.02/1.43 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.43 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.02/1.43 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 550, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.02/1.43 , 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ), ~(
% 1.02/1.43 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.43 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.02/1.43 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 551, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.43 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.43 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool'
% 1.02/1.43 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), X ) ) ), ~( 'c_lessequals'(
% 1.02/1.43 X, 'c_Set_Oinsert'( Y, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 552, [ =( 'c_Set_Oimage'( X, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.43 , Z ), T ), Y, U ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.43 , 'c_Set_Oimage'( X, Z, Y, U ) ), 'c_Set_Oimage'( X, T, Y, U ) ) ), ~(
% 1.02/1.43 'c_lessequals'( T, W, 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_lessequals'( Z
% 1.02/1.43 , W, 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, W, Y, U ) ) ]
% 1.02/1.43 )
% 1.02/1.43 , clause( 553, [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_lessequals'( X,
% 1.02/1.43 'c_Set_Oimage'( Z, T, U, Y ), 'tc_fun'( Y, 'tc_bool' ) ) ), ~(
% 1.02/1.43 'c_Finite__Set_Ofinite'( T, U ) ) ] )
% 1.02/1.43 , clause( 554, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~(
% 1.02/1.43 hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), W ) ) ), ~( 'c_lessequals'(
% 1.02/1.43 'c_Set_Oimage'( Y, W, U, X ), T, 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 555, [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ),
% 1.02/1.43 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.02/1.43 'tc_bool' ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), T ) ) ) ]
% 1.02/1.43 )
% 1.02/1.43 , clause( 556, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.02/1.43 'c_Finite__Set_Ofold__graph'( Z, T, X, U, Y, W ) ) ] )
% 1.02/1.43 , clause( 557, [ ~( =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.02/1.43 ), =( 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ), Y
% 1.02/1.43 ) ] )
% 1.02/1.43 , clause( 558, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( 't_a', X ) ), Y )
% 1.02/1.43 , Z ), 'v_x' ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.43 X ), hAPP( Y, 'v_x' ) ), hAPP( Z, 'v_x' ) ) ) ] )
% 1.02/1.43 , clause( 559, [ 'c_Fun_Oinj__on'( X, 'c_Set_Oimage'( Y, Z, T, U ), U, W )
% 1.02/1.43 , ~( 'c_Fun_Oinj__on'( 'c_Fun_Ocomp'( X, Y, U, W, T ), Z, T, W ) ) ] )
% 1.02/1.43 , clause( 560, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.02/1.43 'tc_bool' ) ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.02/1.43 'tc_bool' ) ), Y ), T ) ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Z ), T ) ) ) ] )
% 1.02/1.43 , clause( 561, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.43 X, 'tc_bool' ) ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.02/1.43 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), T ) ) ) ] )
% 1.02/1.43 , clause( 562, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ) ] )
% 1.02/1.43 , clause( 563, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ] )
% 1.02/1.43 , clause( 564, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ),
% 1.02/1.43 Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.43 Z, 'tc_bool' ) ), T ), 'c_Collect'( X, Z ) ) ) ) ) ] )
% 1.02/1.43 , clause( 565, [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Oid'( Y ), Y, Z, Y ), X ) ] )
% 1.02/1.43 , clause( 566, [ =( 'c_Fun_Ocomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y ) ] )
% 1.02/1.43 , clause( 567, [ 'c_Finite__Set_Ofinite'( 'c_Set_Ovimage'( X, Y, Z, T ), Z
% 1.02/1.43 ), ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 1.02/1.43 'tc_bool' ) ), Z, T ) ), ~( 'c_Finite__Set_Ofinite'( Y, T ) ) ] )
% 1.02/1.43 , clause( 568, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), Y ), Y ) ] )
% 1.02/1.43 , clause( 569, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Y ), Y ) ]
% 1.02/1.43 )
% 1.02/1.43 , clause( 570, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.02/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 1.02/1.43 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.02/1.43 , clause( 571, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' )
% 1.02/1.43 ), ~( 'c_HOL_Oord__class_Oless'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.02/1.43 'c_HOL_Oord__class_Oless'( X, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 572, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.02/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.02/1.43 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 1.02/1.43 , clause( 573, [ =( 'c_Relation_OImage'( X, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.43 , Z ), T ), Y, U ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.43 , 'c_Relation_OImage'( X, Z, Y, U ) ), 'c_Relation_OImage'( X, T, Y, U )
% 1.02/1.43 ) ) ] )
% 1.02/1.43 , clause( 574, [ 'c_Fun_Oinj__on'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U ),
% 1.02/1.43 hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( X, Y ) ), 'c_Set_Oimage'( X,
% 1.02/1.43 'c_HOL_Ominus__class_Ominus'( Z, 'c_Set_Oinsert'( Y,
% 1.02/1.43 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.02/1.43 T, 'tc_bool' ) ), T, U ) ) ), ~( 'c_Fun_Oinj__on'( X, Z, T, U ) ) ] )
% 1.02/1.43 , clause( 575, [ 'c_Fun_Oinj__on'( 'c_Fun_Oid'( X ), Y, X, X ) ] )
% 1.02/1.43 , clause( 576, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 1.02/1.43 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ] )
% 1.02/1.43 , clause( 577, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.43 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.43 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Z, Y,
% 1.02/1.43 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), X ) ] )
% 1.02/1.43 , clause( 578, [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP(
% 1.02/1.43 hAPP( X, W ), U ) ) ] )
% 1.02/1.43 , clause( 579, [ =( hAPP( 'c_COMBK'( X, Y, Z ), T ), X ) ] )
% 1.02/1.43 , clause( 580, [ ~( =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , 'c_Set_Oimage'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( U,
% 1.02/1.43 'tc_bool' ) ), U, X ) ), 'c_Set_Oimage'( Y, 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.43 T, Z, 'tc_fun'( U, 'tc_bool' ) ), U, X ) ),
% 1.02/1.43 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~(
% 1.02/1.43 'c_Fun_Oinj__on'( Y, T, U, X ) ), ~( 'c_Fun_Oinj__on'( Y, Z, U, X ) ),
% 1.02/1.43 'c_Fun_Oinj__on'( Y, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.43 , Z ), T ), U, X ) ] )
% 1.02/1.43 , clause( 581, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , 'c_Set_Oimage'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( U,
% 1.02/1.43 'tc_bool' ) ), U, X ) ), 'c_Set_Oimage'( Y, 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.43 T, Z, 'tc_fun'( U, 'tc_bool' ) ), U, X ) ),
% 1.02/1.43 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.02/1.43 'c_Fun_Oinj__on'( Y, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.43 , Z ), T ), U, X ) ) ] )
% 1.02/1.43 , clause( 582, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.43 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Y,
% 1.02/1.43 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 1.02/1.43 Z, 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 583, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.02/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 1.02/1.43 , clause( 584, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 1.02/1.43 Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.02/1.43 , clause( 585, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.02/1.43 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 1.02/1.43 , clause( 586, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.02/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.02/1.43 )
% 1.02/1.43 , clause( 587, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.43 Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 1.02/1.43 , clause( 588, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 1.02/1.43 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 1.02/1.43 , clause( 589, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.02/1.43 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 1.02/1.43 , clause( 590, [ ~( 'class_HOL_Oord'( X ) ), ~( 'c_lessequals'( Y, Z,
% 1.02/1.43 'tc_fun'( T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_fun'( T, X
% 1.02/1.43 ) ) ) ] )
% 1.02/1.43 , clause( 591, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'(
% 1.02/1.43 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 1.02/1.43 , clause( 592, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ),
% 1.02/1.43 'c_Set_Oimage'( Y, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( T, 'tc_bool'
% 1.02/1.43 ) ), T, X ) ) ) ] )
% 1.02/1.43 , clause( 593, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.02/1.43 =( 'c_Complete__Lattice_OSup__class_OSup'( Y, X ), 'c_Finite__Set_Ofold'(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.02/1.43 'c_Orderings_Obot__class_Obot'( X ), Y, X, X ) ), ~(
% 1.02/1.43 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.02/1.43 , clause( 594, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.02/1.43 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.02/1.43 , T, X ) ) ), =( Y, Z ) ] )
% 1.02/1.43 , clause( 595, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.02/1.43 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.02/1.43 , T, X ) ) ), =( Z, T ) ] )
% 1.02/1.43 , clause( 596, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.43 'c_Finite__Set_Olinorder__class_OMax'( Y, X ),
% 1.02/1.43 'c_Finite__Set_Olinorder__class_OMax'( Z, X ), X ), ~(
% 1.02/1.43 'c_Finite__Set_Ofinite'( Z, X ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.43 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_lessequals'( Y, Z, 'tc_fun'( X,
% 1.02/1.43 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 597, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.43 'c_Finite__Set_Olinorder__class_OMax'( 'c_Set_Oinsert'( Y,
% 1.02/1.43 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X ), Y )
% 1.02/1.43 ] )
% 1.02/1.43 , clause( 598, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.43 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z, T ), 'tc_fun'( T,
% 1.02/1.43 'tc_bool' ) ), 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, U,
% 1.02/1.43 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ] )
% 1.02/1.43 , clause( 599, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.43 X, 'tc_bool' ) ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Z ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.43 X, 'tc_bool' ) ), Y ), T ) ) ) ] )
% 1.02/1.43 , clause( 600, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.02/1.43 'tc_bool' ) ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.43 X, 'tc_bool' ) ), Z ), T ) ) ) ] )
% 1.02/1.43 , clause( 601, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ] )
% 1.02/1.43 , clause( 602, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ] )
% 1.02/1.43 , clause( 603, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ] )
% 1.02/1.43 , clause( 604, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ] )
% 1.02/1.43 , clause( 605, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), Z ), Y ), ~( 'c_lessequals'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ) ]
% 1.02/1.43 )
% 1.02/1.43 , clause( 606, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), Z ), Z ), ~( 'c_lessequals'( Z, Y, 'tc_fun'( X, 'tc_bool' ) ) ) ]
% 1.02/1.43 )
% 1.02/1.43 , clause( 607, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Y ),
% 1.02/1.43 ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.02/1.43 , clause( 608, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =( hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Y ) )
% 1.02/1.43 , 'c_lessequals'( Y, Z, X ) ] )
% 1.02/1.43 , clause( 609, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Z ),
% 1.02/1.43 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 1.02/1.43 , clause( 610, [ 'c_lessequals'( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ), ~( 'c_lessequals'( Z, T,
% 1.02/1.43 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( X,
% 1.02/1.43 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 611, [ 'c_lessequals'( X, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.43 , Z ), X ), 'tc_fun'( Y, 'tc_bool' ) ) ] )
% 1.02/1.43 , clause( 612, [ 'c_lessequals'( X, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.43 , X ), Z ), 'tc_fun'( Y, 'tc_bool' ) ) ] )
% 1.02/1.43 , clause( 613, [ 'c_lessequals'( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ), ~( 'c_lessequals'( Z, T,
% 1.02/1.43 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( X,
% 1.02/1.43 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 614, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.43 'c_lessequals'( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.43 X ), Y ), Z ), T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'(
% 1.02/1.43 Y, T, X ) ) ] )
% 1.02/1.43 , clause( 615, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.43 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), X ) ] )
% 1.02/1.43 , clause( 616, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.43 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ), X ) ] )
% 1.02/1.43 , clause( 617, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.43 'c_lessequals'( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.43 X ), Y ), Z ), T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'(
% 1.02/1.43 Y, T, X ) ) ] )
% 1.02/1.43 , clause( 618, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.43 'c_lessequals'( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.43 X ), Y ), Z ), T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'(
% 1.02/1.43 Y, T, X ) ) ] )
% 1.02/1.43 , clause( 619, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.02/1.43 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ),
% 1.02/1.43 X ) ] )
% 1.02/1.43 , clause( 620, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.02/1.43 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ),
% 1.02/1.43 X ) ] )
% 1.02/1.43 , clause( 621, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.43 'tc_fun'( X, 'tc_bool' ) ), Z ), Y ) ) ] )
% 1.02/1.43 , clause( 622, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), Y ) ) ] )
% 1.02/1.43 , clause( 623, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), Y ) ) ] )
% 1.02/1.43 , clause( 624, [ 'c_Complete__Lattice_Ocomplete__lattice'( X, Y, 'c_COMBC'(
% 1.02/1.43 Z, T, T, 'tc_bool' ), 'c_COMBC'( U, T, T, 'tc_bool' ), W, V0, V1, V2, T )
% 1.02/1.43 , ~( 'c_Complete__Lattice_Ocomplete__lattice'( Y, X, Z, U, V0, W, V2, V1
% 1.02/1.43 , T ) ) ] )
% 1.02/1.43 , clause( 625, [ =( hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.43 , Y ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.02/1.43 Z ), ~( 'c_lessequals'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.43 , clause( 626, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( hAPP(
% 1.02/1.43 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ), hAPP( hAPP(
% 1.02/1.43 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), X ) ] )
% 1.02/1.44 , clause( 627, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 1.02/1.44 , clause( 628, [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 1.02/1.44 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.44 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'c_Set_Oinsert'( X,
% 1.02/1.44 Y, Z ) ) ] )
% 1.02/1.44 , clause( 629, [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 1.02/1.44 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T,
% 1.02/1.44 'tc_bool' ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.02/1.44 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ), hBOOL( hAPP( hAPP(
% 1.02/1.44 'c_in'( T ), Y ), Z ) ) ] )
% 1.02/1.44 , clause( 630, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ) ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ) ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), T ), Y ) ) ) ] )
% 1.02/1.44 , clause( 631, [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z, Y ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 632, [ 'c_Finite__Set_Ofold__graph'( X, Y, 'c_Set_Oinsert'( Z, T
% 1.02/1.44 , U ), hAPP( hAPP( X, Y ), W ), U, U ), hBOOL( hAPP( hAPP( 'c_in'( U ), Z
% 1.02/1.44 ), T ) ), ~( 'c_Finite__Set_Ofold__graph'( X, Z, T, W, U, U ) ), ~(
% 1.02/1.44 'c_OrderedGroup_Oab__semigroup__mult'( X, U ) ) ] )
% 1.02/1.44 , clause( 633, [ =( 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.02/1.44 'tc_fun'( T, 'tc_bool' ) ), T, U ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.44 'c_Set_Oimage'( X, Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U,
% 1.02/1.44 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'(
% 1.02/1.44 'tc_fun'( T, 'tc_bool' ) ), T, U ) ) ] )
% 1.02/1.44 , clause( 634, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~(
% 1.02/1.44 'c_lessequals'( 'c_Set_Oinsert'( Y, T, X ), Z, 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 ) ] )
% 1.02/1.44 , clause( 635, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.02/1.44 =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y, 'c_COMBK'( Z
% 1.02/1.44 , X, T ), T, X ), Z ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T
% 1.02/1.44 , 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 636, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL(
% 1.02/1.44 hAPP( Y, T ) ) ) ] )
% 1.02/1.44 , clause( 637, [ =( 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T
% 1.02/1.44 , U ), U ), 'c_Set_Oimage'( X, Z, T, U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.02/1.44 T ), Y ), Z ) ) ) ] )
% 1.02/1.44 , clause( 638, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.02/1.44 , 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 1.02/1.44 hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ] )
% 1.02/1.44 , clause( 639, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( Z ), T ), X ) ), ~( 'c_lessequals'( X,
% 1.02/1.44 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 640, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.02/1.44 , 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 1.02/1.44 hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ] )
% 1.02/1.44 , clause( 641, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.44 'c_lessequals'( X, 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.44 ), hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), X ) ) ] )
% 1.02/1.44 , clause( 642, [ 'c_lessequals'( 'c_Set_Ovimage'( X, Y, Z, T ),
% 1.02/1.44 'c_Set_Ovimage'( X, U, Z, T ), 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.44 'c_lessequals'( Y, U, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 643, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), 'c_Set_Oinsert'( Z, T, X ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ] )
% 1.02/1.44 , clause( 644, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , 'c_Set_Oinsert'( Y, Z, X ) ), T ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ] )
% 1.02/1.44 , clause( 645, [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'(
% 1.02/1.44 'c_Fun_Oid'( T ), W, T, T, U ) ) ), =( hAPP( X, hAPP( Y, V0 ) ), hAPP( W
% 1.02/1.44 , V0 ) ) ] )
% 1.02/1.44 , clause( 646, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ), Z ),
% 1.02/1.44 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), Y ), Z ) ) ] )
% 1.02/1.44 , clause( 647, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.02/1.44 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), Y ), Z ) ) ] )
% 1.02/1.44 , clause( 648, [ =( 'c_Set_Oimage'( X, Y, Z, Z ), Y ), ~( 'c_Fun_Oinj__on'(
% 1.02/1.44 X, Y, Z, Z ) ), ~( 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, Z ), Y,
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ] )
% 1.02/1.44 , clause( 649, [ ~( =( hAPP( X,
% 1.02/1.44 'c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1'( Y, X
% 1.02/1.44 , Z, T ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) )
% 1.02/1.44 ), =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ),
% 1.02/1.44 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y, X, Z, 'tc_fun'(
% 1.02/1.44 T, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 650, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ] )
% 1.02/1.44 , clause( 651, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ) ] )
% 1.02/1.44 , clause( 652, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ) ] )
% 1.02/1.44 , clause( 653, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ] )
% 1.02/1.44 , clause( 654, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ) ), Z ), T ) ) ) ] )
% 1.02/1.44 , clause( 655, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ) ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Z ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ) ), Y ), T ) ) ) ] )
% 1.02/1.44 , clause( 656, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.44 'c_Finite__Set_Olinorder__class_OMin'( 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X ), Y )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 657, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.02/1.44 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.44 , X ), Z ), Y ) ) ] )
% 1.02/1.44 , clause( 658, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.02/1.44 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.44 , Z ), X ), Y ) ) ] )
% 1.02/1.44 , clause( 659, [ =( 'c_Map_Orestrict__map'( 'c_Map_Orestrict__map'( X, Y, Z
% 1.02/1.44 , T ), U, Z, T ), 'c_Map_Orestrict__map'( X, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.44 , Y ), U ), Z, T ) ) ] )
% 1.02/1.44 , clause( 660, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Z, Y,
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ) ), T ), T ) ] )
% 1.02/1.44 , clause( 661, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), T, Z,
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ) ), Y ) ] )
% 1.02/1.44 , clause( 662, [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U,
% 1.02/1.44 Z, T ) ) ), ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'(
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ), =( Y, U ) ] )
% 1.02/1.44 , clause( 663, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ),
% 1.02/1.44 'c_Orderings_Otop__class_Otop'( X ) ) ), =( Z,
% 1.02/1.44 'c_Orderings_Otop__class_Otop'( X ) ) ] )
% 1.02/1.44 , clause( 664, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ),
% 1.02/1.44 'c_Orderings_Otop__class_Otop'( X ) ) ), =( Y,
% 1.02/1.44 'c_Orderings_Otop__class_Otop'( X ) ) ] )
% 1.02/1.44 , clause( 665, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( Z ), T ), X ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), T )
% 1.02/1.44 , Y ) ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( T, Y, Z ),
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 666, [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 1.02/1.44 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T,
% 1.02/1.44 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ), hBOOL( hAPP(
% 1.02/1.44 hAPP( 'c_in'( T ), Y ), Z ) ) ] )
% 1.02/1.44 , clause( 667, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), Y ), T ), 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 668, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ), T ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), T ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), Z ), T ), 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 669, [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ),
% 1.02/1.44 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.02/1.44 'tc_bool' ) ), Y ) ), =( T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.44 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 670, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' )
% 1.02/1.44 ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), Y ) ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z,
% 1.02/1.44 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 671, [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 1.02/1.44 'tc_fun'( T, 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), Z ) )
% 1.02/1.44 ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 672, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.02/1.44 'c_Finite__Set_Ofold'( 'c_Lattices_Olower__semilattice__class_Oinf'( X )
% 1.02/1.44 , Y, 'c_Set_Oinsert'( Z, T, X ), X, X ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ),
% 1.02/1.44 'c_Finite__Set_Ofold'( 'c_Lattices_Olower__semilattice__class_Oinf'( X )
% 1.02/1.44 , Y, T, X, X ) ) ), ~( 'c_Finite__Set_Ofinite'( T, X ) ) ] )
% 1.02/1.44 , clause( 673, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( T, U, 'tc_fun'(
% 1.02/1.44 Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( U, Y,
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 1.02/1.44 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 674, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ),
% 1.02/1.44 'c_Orderings_Otop__class_Otop'( X ) ), Y ) ] )
% 1.02/1.44 , clause( 675, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ),
% 1.02/1.44 'c_Orderings_Otop__class_Otop'( X ) ), Y ), Y ) ] )
% 1.02/1.44 , clause( 676, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ), Y ), Y )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 677, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ), Y )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 678, [ =( 'c_Set_Oimage'( X, 'c_Set_Ovimage'( X, Y, Z, T ), Z, T
% 1.02/1.44 ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( T
% 1.02/1.44 , 'tc_bool' ) ), Y ), 'c_Set_Oimage'( X, 'c_Orderings_Otop__class_Otop'(
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ) ) ] )
% 1.02/1.44 , clause( 679, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ), X ) ] )
% 1.02/1.44 , clause( 680, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), T ), Z ), 'tc_fun'( X, 'tc_bool' ) ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 681, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 1.02/1.44 'c_lessequals'( Y, Z, X ) ) ] )
% 1.02/1.44 , clause( 682, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_fun'( Y, 'tc_bool'
% 1.02/1.44 ) ) ) ] )
% 1.02/1.44 , clause( 683, [ ~( 'class_HOL_Oord'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 Z, 'tc_fun'( T, X ) ), 'c_lessequals'( Z, Y, 'tc_fun'( T, X ) ), ~(
% 1.02/1.44 'c_lessequals'( Y, Z, 'tc_fun'( T, X ) ) ) ] )
% 1.02/1.44 , clause( 684, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.02/1.44 , clause( 685, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.02/1.44 , clause( 686, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 1.02/1.44 , clause( 687, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), Y ) ] )
% 1.02/1.44 , clause( 688, [ hBOOL( hAPP( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), Y ) ) ] )
% 1.02/1.44 , clause( 689, [ ~( 'class_Orderings_Otop'( X ) ), =( hAPP(
% 1.02/1.44 'c_Orderings_Otop__class_Otop'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 1.02/1.44 'c_Orderings_Otop__class_Otop'( X ) ) ] )
% 1.02/1.44 , clause( 690, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.44 'c_lessequals'( hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z, 'tc_bool' )
% 1.02/1.44 , 'tc_bool' ), X ), hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z,
% 1.02/1.44 'tc_bool' ), 'tc_bool' ), Y ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 691, [ 'c_lessequals'( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ), 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X,
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ), 'tc_bool' ), Z ), 'tc_fun'( X, 'tc_bool' ) ),
% 1.02/1.44 ~( 'c_lessequals'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 692, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.02/1.44 'c_Finite__Set_Ofold'( 'c_Lattices_Oupper__semilattice__class_Osup'( X )
% 1.02/1.44 , Y, 'c_Set_Oinsert'( Z, T, X ), X, X ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ),
% 1.02/1.44 'c_Finite__Set_Ofold'( 'c_Lattices_Oupper__semilattice__class_Osup'( X )
% 1.02/1.44 , Y, T, X, X ) ) ), ~( 'c_Finite__Set_Ofinite'( T, X ) ) ] )
% 1.02/1.44 , clause( 693, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.02/1.44 ), =( Z, Y ) ] )
% 1.02/1.44 , clause( 694, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.44 ) ] )
% 1.02/1.44 , clause( 695, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool'
% 1.02/1.44 ) ) ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 696, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool'
% 1.02/1.44 ) ) ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 697, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.02/1.44 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.02/1.44 , clause( 698, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.02/1.44 ), =( Z, Y ) ] )
% 1.02/1.44 , clause( 699, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.02/1.44 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.02/1.44 , clause( 700, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.02/1.44 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 1.02/1.44 , clause( 701, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 1.02/1.44 , clause( 702, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.02/1.44 ) ] )
% 1.02/1.44 , clause( 703, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), Y ) ] )
% 1.02/1.44 , clause( 704, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), T, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 1.02/1.44 , clause( 705, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), T, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.02/1.44 , clause( 706, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ), hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), Y ), Z ) ), Y ) ] )
% 1.02/1.44 , clause( 707, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 708, [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( Y, Z, 'tc_fun'(
% 1.02/1.44 T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_fun'( T, X ) ) ) ] )
% 1.02/1.44 , clause( 709, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z,
% 1.02/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.02/1.44 , clause( 710, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.02/1.44 , clause( 711, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), Y ),
% 1.02/1.44 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 1.02/1.44 , clause( 712, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), Z ) )
% 1.02/1.44 , 'c_lessequals'( Y, Z, X ) ] )
% 1.02/1.44 , clause( 713, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), Z ),
% 1.02/1.44 ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.02/1.44 , clause( 714, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), Z ), ~( 'c_lessequals'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 715, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), Y ), ~( 'c_lessequals'( Z, Y, 'tc_fun'( X, 'tc_bool' ) ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 716, [ ~( =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), Z ) ), 'c_lessequals'( Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ] )
% 1.02/1.44 , clause( 717, [ 'c_Finite__Set_Ofinite'( 'c_Set_Oimage'( X, Y, Z, T ), T )
% 1.02/1.44 , ~( 'c_Finite__Set_Ofinite'( Y, Z ) ) ] )
% 1.02/1.44 , clause( 718, [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 1.02/1.44 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T,
% 1.02/1.44 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 719, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Finite__Set_Olinorder__class_OMin'( Y, X ),
% 1.02/1.44 'c_Finite__Set_Olinorder__class_OMin'( Z, X ), X ), ~(
% 1.02/1.44 'c_Finite__Set_Ofinite'( Y, X ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_lessequals'( Z, Y, 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 720, [ =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.44 'c_Set_Oinsert'( X, Y, Z ), T, Z, 'tc_fun'( U, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.44 , hAPP( T, X ) ), 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.44 Y, T, Z, 'tc_fun'( U, 'tc_bool' ) ) ) ) ] )
% 1.02/1.44 , clause( 721, [ =( hAPP( X, 'c_Set_Oinsert'( Y, Z, T ) ), hAPP( hAPP( U, Y
% 1.02/1.44 ), hAPP( X, Z ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W, X,
% 1.02/1.44 V0, V1, V2, U, V3, V4, T ) ) ] )
% 1.02/1.44 , clause( 722, [ =( hAPP( X, 'c_Set_Oinsert'( Y, Z, T ) ), hAPP( hAPP( U, Y
% 1.02/1.44 ), hAPP( X, Z ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X, W,
% 1.02/1.44 V0, V1, U, V2, V3, V4, T ) ) ] )
% 1.02/1.44 , clause( 723, [ 'c_Finite__Set_Ofold1Set'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y, Z ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 724, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 1.02/1.44 'c_Hoare__Mirabelle_Ohoare__derivs'( X, T, Z ) ), ~(
% 1.02/1.44 'c_Hoare__Mirabelle_Ohoare__derivs'( T, Y, Z ) ) ] )
% 1.02/1.44 , clause( 725, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , 'c_Set_Oinsert'( Y, Z, X ) ), T ), 'c_Set_Oinsert'( Y, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.02/1.44 , clause( 726, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), 'c_Set_Oinsert'( Z, T, X ) ), 'c_Set_Oinsert'( Z, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), T ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), Y ) ) ) ] )
% 1.02/1.44 , clause( 727, [ =( 'c_Set_Oimage'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U ),
% 1.02/1.44 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ) ) ] )
% 1.02/1.44 , clause( 728, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.44 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.02/1.44 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.44 ) ] )
% 1.02/1.44 , clause( 729, [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W ), hAPP( Y,
% 1.02/1.44 hAPP( X, W ) ) ) ] )
% 1.02/1.44 , clause( 730, [ 'c_lessequals'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), T ), U ), 'tc_fun'( X, 'tc_bool' ) ), ~(
% 1.02/1.44 'c_lessequals'( Z, U, 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_lessequals'( Y
% 1.02/1.44 , T, 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 731, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Y, X )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 732, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Z, X )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 733, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ), X ), ~(
% 1.02/1.44 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.02/1.44 , clause( 734, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ), X ), ~(
% 1.02/1.44 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.02/1.44 , clause( 735, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ), X ), ~(
% 1.02/1.44 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.02/1.44 , clause( 736, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.44 X ), Y ), Z ), Z, X ) ] )
% 1.02/1.44 , clause( 737, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.44 X ), Y ), Z ), Y, X ) ] )
% 1.02/1.44 , clause( 738, [ 'c_lessequals'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), Y, 'tc_fun'( X, 'tc_bool' ) ) ] )
% 1.02/1.44 , clause( 739, [ 'c_lessequals'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), Z, 'tc_fun'( X, 'tc_bool' ) ) ] )
% 1.02/1.44 , clause( 740, [ 'c_lessequals'( X, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'( X, T, 'tc_fun'(
% 1.02/1.44 Y, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 741, [ 'c_lessequals'( X, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'( X, T, 'tc_fun'(
% 1.02/1.44 Y, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 742, [ 'c_lessequals'( X, 'c_Orderings_Otop__class_Otop'(
% 1.02/1.44 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ] )
% 1.02/1.44 , clause( 743, [ ~( 'class_Orderings_Otop'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_Orderings_Otop__class_Otop'( X ), X ) ] )
% 1.02/1.44 , clause( 744, [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Ocomp'( Y, Z, T, U, W ), U, V0
% 1.02/1.44 , W ), 'c_Fun_Ocomp'( 'c_Fun_Ocomp'( X, Y, U, V0, T ), Z, T, V0, W ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 745, [ =( 'c_Set_Oinsert'( X,
% 1.02/1.44 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Z, Y,
% 1.02/1.44 'tc_fun'( T, 'tc_bool' ) ), T ), 'c_Set_Oinsert'( X,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ) ) ] )
% 1.02/1.44 , clause( 746, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ] )
% 1.02/1.44 , clause( 747, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ] )
% 1.02/1.44 , clause( 748, [ ~( 'class_HOL_Ominus'( X ) ), =( hAPP(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( hAPP( Y, 'v_x' ), hAPP( Z, 'v_x' ), X ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 749, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.44 'c_lessequals'( X, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.44 , T ), Y ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 750, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.44 'c_lessequals'( X, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.44 , Y ), T ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 751, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ), X ) ) ] )
% 1.02/1.44 , clause( 752, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), T ), Z ), X ) ) ] )
% 1.02/1.44 , clause( 753, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.44 X ), Y ), Z ), T, X ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.02/1.44 , clause( 754, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.44 X ), Y ), Z ), T, X ), ~( 'c_lessequals'( Z, T, X ) ) ] )
% 1.02/1.44 , clause( 755, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ), X ) ) ] )
% 1.02/1.44 , clause( 756, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), T ), Z ), X ) ) ] )
% 1.02/1.44 , clause( 757, [ =( 'c_Set_Ovimage'( 'c_Fun_Oid'( X ), Y, X, X ), Y ) ] )
% 1.02/1.44 , clause( 758, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) ) ] )
% 1.02/1.44 , clause( 759, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_Finite__Set_Ofold'(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y, Z, X, X ), hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), T ), Y ), X ),
% 1.02/1.44 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Z ) ) ), ~(
% 1.02/1.44 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.02/1.44 , clause( 760, [ =( 'c_Set_Ovimage'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U,
% 1.02/1.44 T ), 'c_Set_Ovimage'( Y, 'c_Set_Ovimage'( X, W, Z, T ), U, Z ) ) ] )
% 1.02/1.44 , clause( 761, [ =( 'c_Set_Oinsert'( X, Y, Z ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.44 , 'c_Collect'( hAPP( 'c_COMBC'( 'c_fequal'( Z ), Z, Z, 'tc_bool' ), X ),
% 1.02/1.44 Z ) ), Y ) ) ] )
% 1.02/1.44 , clause( 762, [ 'c_HOL_Oord__class_Oless'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 1.02/1.44 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T,
% 1.02/1.44 'tc_bool' ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.02/1.44 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 763, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), Z ), Y ) ) ] )
% 1.02/1.44 , clause( 764, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ) ) ] )
% 1.02/1.44 , clause( 765, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ) ) ] )
% 1.02/1.44 , clause( 766, [ =( 'c_Set_Oimage'( 'c_Fun_Oid'( X ), Y, X, X ), Y ) ] )
% 1.02/1.44 , clause( 767, [ =( 'c_Set_Oinsert'( X, Y, Z ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.44 , 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.44 'tc_bool' ) ), Z ) ), Y ) ) ] )
% 1.02/1.44 , clause( 768, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ) ) ] )
% 1.02/1.44 , clause( 769, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ] )
% 1.02/1.44 , clause( 770, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ] )
% 1.02/1.44 , clause( 771, [ 'c_Finite__Set_Ofold__graph'( X, Y, 'c_Set_Oinsert'( Z,
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( T, 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ), U ), 'tc_fun'(
% 1.02/1.44 U, 'tc_bool' ) ), U ), W, U, U ), hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T
% 1.02/1.44 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Y ), T ) ) ), ~(
% 1.02/1.44 'c_Finite__Set_Ofold__graph'( X, Z, T, W, U, U ) ), ~(
% 1.02/1.44 'c_OrderedGroup_Oab__semigroup__mult'( X, U ) ) ] )
% 1.02/1.44 , clause( 772, [ 'c_Fun_Oinj__on'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U, T
% 1.02/1.44 ), ~( 'c_Fun_Oinj__on'( X, 'c_Set_Oimage'( Y, W, U, Z ), Z, T ) ), ~(
% 1.02/1.44 'c_Fun_Oinj__on'( Y, W, U, Z ) ) ] )
% 1.02/1.44 , clause( 773, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 774, [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ),
% 1.02/1.44 'c_Finite__Set_Ofinite'( Y, X ) ] )
% 1.02/1.44 , clause( 775, [ 'c_Finite__Set_Ofold__graph'( X, Y, 'c_Set_Oinsert'( Z, T
% 1.02/1.44 , U ), hAPP( hAPP( X, Z ), W ), U, V0 ), ~( 'c_Finite__Set_Ofold__graph'(
% 1.02/1.44 X, Y, T, W, U, V0 ) ), hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ] )
% 1.02/1.44 , clause( 776, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.02/1.44 hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Z ), 'c_Collect'( T, X ) ) ) ) ) ] )
% 1.02/1.44 , clause( 777, [ =( 'c_Set_Ovimage'( X, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ), U, Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.44 , 'c_Set_Ovimage'( X, Z, U, Y ) ), 'c_Set_Ovimage'( X, T, U, Y ) ) ) ] )
% 1.02/1.44 , clause( 778, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.02/1.44 =( 'c_Complete__Lattice_OSup__class_OSup'( 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), X ), X ), X ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ] )
% 1.02/1.44 , clause( 779, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ),
% 1.02/1.44 'c_Set_Oimage'( Y, 'c_HOL_Ominus__class_Ominus'( T, 'c_Set_Oinsert'( Z,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ), U ), 'tc_fun'(
% 1.02/1.44 U, 'tc_bool' ) ), U, X ) ) ) ), ~( 'c_Fun_Oinj__on'( Y, 'c_Set_Oinsert'(
% 1.02/1.44 Z, T, U ), U, X ) ) ] )
% 1.02/1.44 , clause( 780, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z
% 1.02/1.44 ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), Z ) ),
% 1.02/1.44 hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ] )
% 1.02/1.44 , clause( 781, [ 'c_Nitpick_Ofold__graph_H'( X, Y, Z, hAPP( hAPP( X, T ), U
% 1.02/1.44 ), W, V0 ), ~( 'c_Nitpick_Ofold__graph_H'( X, Y,
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Z, 'c_Set_Oinsert'( T,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( W, 'tc_bool' ) ), W ), 'tc_fun'(
% 1.02/1.44 W, 'tc_bool' ) ), U, W, V0 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( W ), T ), Z
% 1.02/1.44 ) ) ) ] )
% 1.02/1.44 , clause( 782, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T
% 1.02/1.44 , 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 1.02/1.44 ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 1.02/1.44 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 783, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.44 , T ), X ), Y ) ) ) ] )
% 1.02/1.44 , clause( 784, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.44 , X ), T ), Y ) ) ) ] )
% 1.02/1.44 , clause( 785, [ 'c_Fun_Oinj__on'( X, Y, Z, Z ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_Set_Oimage'( X, Y, Z, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.02/1.44 'c_Finite__Set_Ofinite'( Y, Z ) ) ] )
% 1.02/1.44 , clause( 786, [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X,
% 1.02/1.44 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z,
% 1.02/1.44 'tc_bool' ) ), U ), Y ), Z, T ) ) ] )
% 1.02/1.44 , clause( 787, [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X,
% 1.02/1.44 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z,
% 1.02/1.44 'tc_bool' ) ), Y ), U ), Z, T ) ) ] )
% 1.02/1.44 , clause( 788, [ 'c_lessequals'( 'c_Set_Ovimage'( X, Y, Z, T ), U, 'tc_fun'(
% 1.02/1.44 Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, 'c_Set_Oimage'( X, U, Z, T ),
% 1.02/1.44 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X,
% 1.02/1.44 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ) ] )
% 1.02/1.44 , clause( 789, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.02/1.44 =( 'c_Complete__Lattice_OSup__class_OSup'( 'c_Orderings_Otop__class_Otop'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), X ), 'c_Orderings_Otop__class_Otop'( X ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 790, [ =( hAPP( 'c_Fun_Oid'( X ), Y ), Y ) ] )
% 1.02/1.44 , clause( 791, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.44 'c_lessequals'( X, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.02/1.44 , Y ), T ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 792, [ 'c_lessequals'( X, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ), T,
% 1.02/1.44 'tc_fun'( Y, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 793, [ 'c_Finite__Set_Ofinite'( X, 't_a' ), ~(
% 1.02/1.44 'c_Wellfounded_Omax__extp'( Y, Z, X, 't_a' ) ) ] )
% 1.02/1.44 , clause( 794, [ 'c_Finite__Set_Ofinite'( X, 't_a' ), ~(
% 1.02/1.44 'c_Wellfounded_Omax__extp'( Y, X, Z, 't_a' ) ) ] )
% 1.02/1.44 , clause( 795, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.02/1.44 , clause( 796, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.02/1.44 , clause( 797, [ =( 'c_Set_Ovimage'( X, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ), U, Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.44 , 'c_Set_Ovimage'( X, Z, U, Y ) ), 'c_Set_Ovimage'( X, T, U, Y ) ) ) ] )
% 1.02/1.44 , clause( 798, [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.02/1.44 , clause( 799, [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.02/1.44 , clause( 800, [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( hAPP( Y, Z ),
% 1.02/1.44 hAPP( T, Z ), X ), ~( 'c_lessequals'( Y, T, 'tc_fun'( U, X ) ) ) ] )
% 1.02/1.44 , clause( 801, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.02/1.44 , clause( 802, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.02/1.44 , clause( 803, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T
% 1.02/1.44 , X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.02/1.44 , clause( 804, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T
% 1.02/1.44 , X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.02/1.44 , clause( 805, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.02/1.44 hAPP( 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 806, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~(
% 1.02/1.44 'c_lessequals'( T, Z, 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.44 'c_in'( X ), Y ), T ) ) ) ] )
% 1.02/1.44 , clause( 807, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.02/1.44 hAPP( 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 808, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.02/1.44 hAPP( 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 809, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.02/1.44 , clause( 810, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.02/1.44 , clause( 811, [ =( hAPP( 'c_Map_Orestrict__map'( X, Y, Z, T ), U ), hAPP(
% 1.02/1.44 X, U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), Y ) ) ) ] )
% 1.02/1.44 , clause( 812, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), =( Y, T ), ~(
% 1.02/1.44 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( T, Z, X ) ) ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 813, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), hBOOL( hAPP(
% 1.02/1.44 hAPP( 'c_in'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.44 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), T ), Z ) ) ) ) ] )
% 1.02/1.44 , clause( 814, [ =( hAPP( 'c_Fun_Ooverride__on'( X, Y, Z, T, U ), W ), hAPP(
% 1.02/1.44 Y, W ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), W ), Z ) ) ) ] )
% 1.02/1.44 , clause( 815, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.44 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ] )
% 1.02/1.44 , clause( 816, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( T, Z,
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.02/1.44 , clause( 817, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.02/1.44 hAPP( 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ) ) ) ) ] )
% 1.02/1.44 , clause( 818, [ =( hAPP( 'c_Fun_Ooverride__on'( X, Y, Z, T, U ), W ), hAPP(
% 1.02/1.44 X, W ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), W ), Z ) ) ] )
% 1.02/1.44 , clause( 819, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.02/1.44 hAPP( 'c_in'( X ), Y ), T ) ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z,
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 820, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z
% 1.02/1.44 , X ) ) ) ] )
% 1.02/1.44 , clause( 821, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z
% 1.02/1.44 , X ) ) ) ] )
% 1.02/1.44 , clause( 822, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z
% 1.02/1.44 , X ) ) ) ] )
% 1.02/1.44 , clause( 823, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.02/1.44 hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , T ), Z ) ) ) ) ] )
% 1.02/1.44 , clause( 824, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.02/1.44 hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ) ) ) ) ] )
% 1.02/1.44 , clause( 825, [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.44 'c_in'( T ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), U ) )
% 1.02/1.44 ), =( Y, Z ), ~( 'c_Fun_Oinj__on'( X, U, T, W ) ) ] )
% 1.02/1.44 , clause( 826, [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.44 'c_in'( T ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), U ) )
% 1.02/1.44 ), ~( 'c_Fun_Oinj__on'( X, U, T, W ) ), =( Y, Z ) ] )
% 1.02/1.44 , clause( 827, [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.44 'c_in'( T ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), U ) )
% 1.02/1.44 ), ~( 'c_Fun_Oinj__on'( X, U, T, W ) ), =( Y, Z ) ] )
% 1.02/1.44 , clause( 828, [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( 'c_Fun_Oinj__on'(
% 1.02/1.44 X, T, U, W ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) )
% 1.02/1.44 ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Y ), T ) ) ) ] )
% 1.02/1.44 , clause( 829, [ ~( =( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ), 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ), 'tc_bool' ), Z ) ) ), =( Y, Z ) ] )
% 1.02/1.44 , clause( 830, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Collect'( Z, X ) )
% 1.02/1.44 ), ~( hBOOL( hAPP( Z, Y ) ) ) ] )
% 1.02/1.44 , clause( 831, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ),
% 1.02/1.44 Y ), 'c_Collect'( X, Z ) ) ) ) ] )
% 1.02/1.44 , clause( 832, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y
% 1.02/1.44 ), Z ) ) ) ] )
% 1.02/1.44 , clause( 833, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y
% 1.02/1.44 ), Z ) ) ) ] )
% 1.02/1.44 , clause( 834, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z
% 1.02/1.44 ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ), hBOOL( hAPP( hAPP(
% 1.02/1.44 'c_in'( Z ), X ), Y ) ), =( Y, T ) ] )
% 1.02/1.44 , clause( 835, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.44 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, T, U, 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( T, W
% 1.02/1.44 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), Z ) ) ) ] )
% 1.02/1.44 , clause( 836, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.44 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, T, U, 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( T, W
% 1.02/1.44 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), Z ) ) ) ] )
% 1.02/1.44 , clause( 837, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T
% 1.02/1.44 , X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 838, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T
% 1.02/1.44 , X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 839, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T
% 1.02/1.44 , X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 840, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~(
% 1.02/1.44 hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 841, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~(
% 1.02/1.44 hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 842, [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( U ), T ), Z ) ) ), ~(
% 1.02/1.44 'c_Complete__Lattice_Ocomplete__lattice'( Y, W, X, V0, V1, V2, V3, V4, U
% 1.02/1.44 ) ) ] )
% 1.02/1.44 , clause( 843, [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( U ), Y ), T ) ) ), ~(
% 1.02/1.44 'c_Complete__Lattice_Ocomplete__lattice'( W, Z, X, V0, V1, V2, V3, V4, U
% 1.02/1.44 ) ) ] )
% 1.02/1.44 , clause( 844, [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.44 'c_in'( Z ), X ), Y ) ) ) ] )
% 1.02/1.44 , clause( 845, [ hBOOL( hAPP(
% 1.02/1.44 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, Y, Z, 'tc_fun'(
% 1.02/1.44 T, 'tc_bool' ) ), U ) ), ~( hBOOL( hAPP( hAPP( Y, W ), U ) ) ), ~( hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( Z ), W ), X ) ) ) ] )
% 1.02/1.44 , clause( 846, [ hBOOL( hAPP(
% 1.02/1.44 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, Y, Z, 'tc_fun'(
% 1.02/1.44 T, 'tc_bool' ) ), U ) ), ~( hBOOL( hAPP( hAPP( Y, W ), U ) ) ), ~( hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( Z ), W ), X ) ) ) ] )
% 1.02/1.44 , clause( 847, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 848, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ) ), Z ), T ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), T ) ) ) ] )
% 1.02/1.44 , clause( 849, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), Y ), T ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ) ) ) ] )
% 1.02/1.44 , clause( 850, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ] )
% 1.02/1.44 , clause( 851, [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z
% 1.02/1.44 , 'tc_bool' ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ),
% 1.02/1.44 ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ) ] )
% 1.02/1.44 , clause( 852, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ) ] )
% 1.02/1.44 , clause( 853, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ) ] )
% 1.02/1.44 , clause( 854, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ) ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ) ) ] )
% 1.02/1.44 , clause( 855, [ =( hAPP( hAPP( X, Y ), hAPP( Z, T ) ),
% 1.02/1.44 'c_Finite__Set_Ofold'( X, Y, T, U, U ) ), ~( 'c_Finite__Set_Ofinite'( T,
% 1.02/1.44 U ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W, Z, V0, V1, V2, X,
% 1.02/1.44 V3, V4, U ) ) ] )
% 1.02/1.44 , clause( 856, [ =( hAPP( hAPP( X, Y ), hAPP( Z, T ) ),
% 1.02/1.44 'c_Finite__Set_Ofold'( X, Y, T, U, U ) ), ~( 'c_Finite__Set_Ofinite'( T,
% 1.02/1.44 U ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( Z, W, V0, V1, X, V2,
% 1.02/1.44 V3, V4, U ) ) ] )
% 1.02/1.44 , clause( 857, [ =( hAPP( X, Y ), 'c_Finite__Set_Ofold'( Z, T, Y, U, U ) )
% 1.02/1.44 , ~( 'c_Finite__Set_Ofinite'( Y, U ) ), ~(
% 1.02/1.44 'c_Complete__Lattice_Ocomplete__lattice'( W, X, V0, V1, V2, Z, T, V3, U )
% 1.02/1.44 ) ] )
% 1.02/1.44 , clause( 858, [ =( hAPP( X, Y ), 'c_Finite__Set_Ofold'( Z, T, Y, U, U ) )
% 1.02/1.44 , ~( 'c_Finite__Set_Ofinite'( Y, U ) ), ~(
% 1.02/1.44 'c_Complete__Lattice_Ocomplete__lattice'( X, W, V0, V1, Z, V2, V3, T, U )
% 1.02/1.44 ) ] )
% 1.02/1.44 , clause( 859, [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.44 Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z
% 1.02/1.44 , 'tc_bool' ) ), Z ) ) ] )
% 1.02/1.44 , clause( 860, [ 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.44 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), T ), ~(
% 1.02/1.44 'c_Finite__Set_Ofinite'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T
% 1.02/1.44 , 'tc_bool' ) ), T ) ) ] )
% 1.02/1.44 , clause( 861, [ =( 'c_Fun_Ofcomp'( X, 'c_Fun_Oid'( Y ), Z, Y, Y ), X ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 862, [ =( 'c_Fun_Ofcomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 863, [ =( 'c_Set_Oimage'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U, T
% 1.02/1.44 ), 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, W, U, Z ), Z, T ) ) ] )
% 1.02/1.44 , clause( 864, [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ),
% 1.02/1.44 'c_Finite__Set_Ofinite'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), X ) ] )
% 1.02/1.44 , clause( 865, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 1.02/1.44 , clause( 866, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 1.02/1.44 , clause( 867, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.02/1.44 =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ),
% 1.02/1.44 'c_Complete__Lattice_OSup__class_OSup'( Z, X ) ), 'c_Finite__Set_Ofold'(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y, Z, X, X ) ), ~(
% 1.02/1.44 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.02/1.44 , clause( 868, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Y ), Y ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 869, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Y ), Y ) ] )
% 1.02/1.44 , clause( 870, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), T ), Y ), Z, X ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 871, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ), Z, X ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 872, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ), X ), ~(
% 1.02/1.44 'c_lessequals'( Y, T, X ) ) ] )
% 1.02/1.44 , clause( 873, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ), X ), ~(
% 1.02/1.44 'c_lessequals'( Y, Z, X ) ) ] )
% 1.02/1.44 , clause( 874, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), T ), Y ), Z, X ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 875, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ), Z, X ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 876, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.44 'c_lessequals'( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ), X ), T ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 877, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.44 'c_lessequals'( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ), T ), X ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 878, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( 't_a', X ) ), Y )
% 1.02/1.44 , Z ), 'v_x' ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.44 X ), hAPP( Y, 'v_x' ) ), hAPP( Z, 'v_x' ) ) ) ] )
% 1.02/1.44 , clause( 879, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z,
% 1.02/1.44 X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 1.02/1.44 , clause( 880, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 1.02/1.44 , clause( 881, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.02/1.44 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 1.02/1.44 , clause( 882, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 883, [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ] )
% 1.02/1.44 , clause( 884, [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ] )
% 1.02/1.44 , clause( 885, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 1.02/1.44 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 1.02/1.44 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 886, [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_lessequals'( Y, U,
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, U, Z, T ) ) ] )
% 1.02/1.44 , clause( 887, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( Z, Y ) ) ), ~(
% 1.02/1.44 'c_lessequals'( Z, X, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 888, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y,
% 1.02/1.44 X ) ] )
% 1.02/1.44 , clause( 889, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 Y, X ) ] )
% 1.02/1.44 , clause( 890, [ 'c_Finite__Set_Ofinite'( X, Y ), ~(
% 1.02/1.44 'c_Finite__Set_Ofinite'( Z, Y ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( Y,
% 1.02/1.44 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 891, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' )
% 1.02/1.44 ), ~( 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( X, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 892, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' )
% 1.02/1.44 ), ~( 'c_HOL_Oord__class_Oless'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 1.02/1.44 'c_lessequals'( X, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 893, [ hBOOL( hAPP( X, Y ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'(
% 1.02/1.44 T, 'tc_bool' ) ) ), ~( hBOOL( hAPP( Z, Y ) ) ) ] )
% 1.02/1.44 , clause( 894, [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_lessequals'( X, Z,
% 1.02/1.44 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ] )
% 1.02/1.44 , clause( 895, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 1.02/1.44 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.02/1.44 , clause( 896, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.02/1.44 , clause( 897, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.02/1.44 =( 'c_Complete__Lattice_OSup__class_OSup'( 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X ), Y )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 898, [ 'c_lessequals'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), T ), U ), 'tc_fun'( X, 'tc_bool' ) ), ~(
% 1.02/1.44 'c_lessequals'( Z, U, 'tc_fun'( X, 'tc_bool' ) ) ), ~( 'c_lessequals'( Y
% 1.02/1.44 , T, 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 899, [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.44 , 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Y, 'tc_bool' ) ) ) ) ] )
% 1.02/1.44 , clause( 900, [ =( 'c_Collect'( hAPP( 'c_COMBC'( 'c_fequal'( X ), X, X,
% 1.02/1.44 'tc_bool' ), Y ), X ), 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), X ) ) ] )
% 1.02/1.44 , clause( 901, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), T, 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 902, [ =( 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.02/1.44 'tc_fun'( T, 'tc_bool' ) ), T, U ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.44 'c_Set_Oimage'( X, Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U,
% 1.02/1.44 'tc_bool' ) ) ), ~( 'c_lessequals'( Z, W, 'tc_fun'( T, 'tc_bool' ) ) ),
% 1.02/1.44 ~( 'c_lessequals'( Y, W, 'tc_fun'( T, 'tc_bool' ) ) ), ~(
% 1.02/1.44 'c_Fun_Oinj__on'( X, W, T, U ) ) ] )
% 1.02/1.44 , clause( 903, [ =( hAPP( X, 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), Y ),
% 1.02/1.44 ~( 'c_Complete__Lattice_Ocomplete__lattice'( T, X, U, W, V0, V1, V2, V3,
% 1.02/1.44 Z ) ) ] )
% 1.02/1.44 , clause( 904, [ =( hAPP( X, 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), Y ),
% 1.02/1.44 ~( 'c_Complete__Lattice_Ocomplete__lattice'( X, T, U, W, V0, V1, V2, V3,
% 1.02/1.44 Z ) ) ] )
% 1.02/1.44 , clause( 905, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Z ), 'c_Collect'( T, X ) ) ) ), ~( hBOOL( hAPP( T, Y ) ) ), ~( hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.02/1.44 , clause( 906, [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( W, V0
% 1.02/1.44 , V1, T, U ) ) ), =( hAPP( X, hAPP( Y, V2 ) ), hAPP( W, hAPP( V0, V2 ) )
% 1.02/1.44 ) ] )
% 1.02/1.44 , clause( 907, [ ~( =( hAPP( X, hAPP( Y, Z ) ), hAPP( T, hAPP( U, W ) ) ) )
% 1.02/1.44 , =( hAPP( 'c_Fun_Ocomp'( X, Y, V0, V1, V2 ), Z ), hAPP( 'c_Fun_Ocomp'( T
% 1.02/1.44 , U, V3, V1, V4 ), W ) ) ] )
% 1.02/1.44 , clause( 908, [ =( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), =( X, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.02/1.44 Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 909, [ =( 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Y, Z, T ), U, T )
% 1.02/1.44 , hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U,
% 1.02/1.44 'tc_bool' ) ), 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), U, T ) )
% 1.02/1.44 , 'c_Set_Ovimage'( X, Z, U, T ) ) ) ] )
% 1.02/1.44 , clause( 910, [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ), 'tc_fun'( Y, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.44 , 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Y, 'tc_bool' ) ) ) ) ] )
% 1.02/1.44 , clause( 911, [ =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.44 hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), Y ), Z ), T, X, 'tc_fun'( U, 'tc_bool' ) ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.44 , 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y, T, X,
% 1.02/1.44 'tc_fun'( U, 'tc_bool' ) ) ),
% 1.02/1.44 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, T, X, 'tc_fun'(
% 1.02/1.44 U, 'tc_bool' ) ) ) ) ] )
% 1.02/1.44 , clause( 912, [ hBOOL( hAPP( X, hAPP( Y, Z ) ) ), ~( hBOOL( hAPP(
% 1.02/1.44 'c_Set_Ovimage'( Y, X, T, U ), Z ) ) ) ] )
% 1.02/1.44 , clause( 913, [ hBOOL( hAPP( 'c_Set_Ovimage'( X, Y, Z, T ), U ) ), ~(
% 1.02/1.44 hBOOL( hAPP( Y, hAPP( X, U ) ) ) ) ] )
% 1.02/1.44 , clause( 914, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Finite__Set_Olinorder__class_OMin'( Y, X ), Z, X ), ~( hBOOL( hAPP(
% 1.02/1.44 hAPP( 'c_in'( X ), Z ), Y ) ) ), ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 915, [ =( 'c_Finite__Set_Ofold__image'( X, Y, Z, 'c_Set_Oinsert'(
% 1.02/1.44 T, U, W ), V0, W ), hAPP( hAPP( X, hAPP( Y, T ) ),
% 1.02/1.44 'c_Finite__Set_Ofold__image'( X, Y, Z, U, V0, W ) ) ), hBOOL( hAPP( hAPP(
% 1.02/1.44 'c_in'( W ), T ), U ) ), ~( 'c_Finite__Set_Ofinite'( U, W ) ), ~(
% 1.02/1.44 'c_OrderedGroup_Oab__semigroup__mult'( X, V0 ) ) ] )
% 1.02/1.44 , clause( 916, [ hBOOL( hAPP( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), T ) ), ~( hBOOL( hAPP( Z, T ) ) ), ~( hBOOL( hAPP( Y, T ) ) )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 917, [ =( 'c_Set_Ovimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ),
% 1.02/1.44 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z, 'tc_bool' ) ) ), ~( hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( Y ), X ), T ) ) ) ] )
% 1.02/1.44 , clause( 918, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 1.02/1.44 T, 'tc_bool' ) ), Z ), ~( 'c_lessequals'( X, Y, 'tc_fun'( T, 'tc_bool' )
% 1.02/1.44 ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 919, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.44 ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 1.02/1.44 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 1.02/1.44 , clause( 920, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.44 ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 1.02/1.44 ~( 'c_lessequals'( U, T, X ) ) ] )
% 1.02/1.44 , clause( 921, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.44 ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 1.02/1.44 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.02/1.44 , clause( 922, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.44 ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 1.02/1.44 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 1.02/1.44 , clause( 923, [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ),
% 1.02/1.44 'c_Set_Oimage'( X, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 1.02/1.44 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 924, [ ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ),
% 1.02/1.44 'c_lessequals'( 'c_Set_Oimage'( T, X, Z, U ), 'c_Set_Oimage'( T, Y, Z, U
% 1.02/1.44 ), 'tc_fun'( U, 'tc_bool' ) ) ] )
% 1.02/1.44 , clause( 925, [ =( 'c_Collect'( hAPP( 'c_fequal'( X ), Y ), X ),
% 1.02/1.44 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), X ) ) ] )
% 1.02/1.44 , clause( 926, [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ),
% 1.02/1.44 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 1.02/1.44 Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 927, [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Fun_Oinj__on'( Z, X
% 1.02/1.44 , Y, T ) ), ~( 'c_Finite__Set_Ofinite'( 'c_Set_Oimage'( Z, X, Y, T ), T )
% 1.02/1.44 ) ] )
% 1.02/1.44 , clause( 928, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 1.02/1.44 , X ) ) ] )
% 1.02/1.44 , clause( 929, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 1.02/1.44 Z, Y ) ] )
% 1.02/1.44 , clause( 930, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z, 'tc_bool' )
% 1.02/1.44 ), =( X, Y ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 931, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.02/1.44 , clause( 932, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.02/1.44 , X ) ) ] )
% 1.02/1.44 , clause( 933, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_fun'( Z,
% 1.02/1.44 'tc_bool' ) ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 934, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.02/1.44 , X ) ) ] )
% 1.02/1.44 , clause( 935, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 1.02/1.44 Y, Z ) ] )
% 1.02/1.44 , clause( 936, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 1.02/1.44 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 1.02/1.44 , clause( 937, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.02/1.44 , clause( 938, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_Finite__Set_Olinorder__class_OMax'( Z, X ), X ), ~( hBOOL( hAPP( hAPP(
% 1.02/1.44 'c_in'( X ), Y ), Z ) ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ] )
% 1.02/1.44 , clause( 939, [ =( 'c_Set_Oimage'( X, hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.44 , Z ), T ), Y, U ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( U, 'tc_bool' ) )
% 1.02/1.44 , 'c_Set_Oimage'( X, Z, Y, U ) ), 'c_Set_Oimage'( X, T, Y, U ) ) ) ] )
% 1.02/1.44 , clause( 940, [ =( 'c_Collect'( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ), 'tc_bool' ), Y ), X ), Y ) ] )
% 1.02/1.44 , clause( 941, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, 'c_Complete__Lattice_OSup__class_OSup'( Z, X ), X ),
% 1.02/1.44 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.02/1.44 , clause( 942, [ =( 'c_Fun_Ofcomp'( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W, Z,
% 1.02/1.44 U, V0 ), 'c_Fun_Ofcomp'( X, 'c_Fun_Ofcomp'( Y, W, T, U, V0 ), Z, T, V0 )
% 1.02/1.44 ) ] )
% 1.02/1.44 , clause( 943, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.44 Y, X ) ) ] )
% 1.02/1.44 , clause( 944, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.44 Y, X ) ) ] )
% 1.02/1.44 , clause( 945, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 1.02/1.44 , clause( 946, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.44 Y, X ) ) ] )
% 1.02/1.44 , clause( 947, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.44 Y, X ) ) ] )
% 1.02/1.44 , clause( 948, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 949, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ),
% 1.02/1.44 'c_Set_Oimage'( Y, T, U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z )
% 1.02/1.44 , T ) ) ) ] )
% 1.02/1.44 , clause( 950, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ),
% 1.02/1.44 'c_Set_Oimage'( Y, T, U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z )
% 1.02/1.44 , T ) ) ) ] )
% 1.02/1.44 , clause( 951, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.02/1.44 'c_in'( X ), 'c_Finite__Set_Olinorder__class_OMin'( Y, X ) ), Y ) ), =( Y
% 1.02/1.44 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.02/1.44 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.02/1.44 , clause( 952, [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.02/1.44 'c_in'( X ), 'c_Finite__Set_Olinorder__class_OMax'( Y, X ) ), Y ) ), =( Y
% 1.02/1.44 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.02/1.44 'c_Finite__Set_Ofinite'( Y, X ) ) ] )
% 1.02/1.44 , clause( 953, [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 1.02/1.44 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.44 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y ), ~( hBOOL( hAPP(
% 1.02/1.44 hAPP( 'c_in'( Z ), X ), Y ) ) ) ] )
% 1.02/1.44 , clause( 954, [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y
% 1.02/1.44 ), 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Z,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ), U ), T, U ) )
% 1.02/1.44 ) ) ] )
% 1.02/1.44 , clause( 955, [ =( 'c_Set_Ovimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.02/1.44 hAPP( 'c_in'( Y ), X ), T ) ) ] )
% 1.02/1.44 , clause( 956, [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.02/1.44 ) ), 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y, Z, T,
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ),
% 1.02/1.44 'c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1'( Y, Z
% 1.02/1.44 , T, X ) ), Y ) ) ] )
% 1.02/1.44 , clause( 957, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 1.02/1.44 'c_Set_Oinsert'( hAPP( Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.02/1.44 T, 'tc_bool' ) ), T ), X, T ) ) ) ] )
% 1.02/1.44 , clause( 958, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.02/1.44 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1'(
% 1.02/1.44 Y, X ) ),
% 1.02/1.44 'c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2'(
% 1.02/1.44 Y, X ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 959, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( Z ), X ), Y ) ), ~(
% 1.02/1.44 'c_OrderedGroup_Oab__semigroup__mult'( T, U ) ) ] )
% 1.02/1.44 , clause( 960, [ =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.02/1.44 X, Y, Z, 'tc_fun'( T, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( T, 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ),
% 1.02/1.44 'c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1'( X, Y
% 1.02/1.44 , Z, T ) ), X ) ) ] )
% 1.02/1.44 , clause( 961, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z
% 1.02/1.44 ), 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.44 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Y ), hBOOL( hAPP( hAPP(
% 1.02/1.44 'c_in'( Z ), X ), Y ) ) ] )
% 1.02/1.44 , clause( 962, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.02/1.44 , hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.02/1.44 'c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2'( Y, Z, X ) )
% 1.02/1.44 , Z ) ) ] )
% 1.02/1.44 , clause( 963, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.02/1.44 , hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.02/1.44 'c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1'( Y, Z, X ) )
% 1.02/1.44 , Y ) ) ] )
% 1.02/1.44 , clause( 964, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( X ) ), Y ), Y ) ] )
% 1.02/1.44 , clause( 965, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( X ) ), Y ) ] )
% 1.02/1.44 , clause( 966, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( X ) ), Y ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.02/1.44 , clause( 967, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( X ) ), 'c_Orderings_Obot__class_Obot'( X
% 1.02/1.44 ) ) ] )
% 1.02/1.44 , clause( 968, [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ] )
% 1.02/1.44 , clause( 969, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.02/1.44 , clause( 970, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =( hAPP(
% 1.02/1.44 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.02/1.44 , clause( 971, [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Y, 'tc_bool' ) ), Z, Y ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 972, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 973, [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ) ), =( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 974, [ =( hAPP( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.02/1.44 'tc_bool' ) ) ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X, T,
% 1.02/1.44 U, W, V0, V1, V2, Z, Y ) ) ] )
% 1.02/1.44 , clause( 975, [ =( hAPP( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.02/1.44 'tc_bool' ) ) ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( T, X,
% 1.02/1.44 U, W, V0, V1, Z, V2, Y ) ) ] )
% 1.02/1.44 , clause( 976, [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), 'c_Collect'( Y, X ) ) ), ~( hBOOL( hAPP( Y, Z ) ) ) ] )
% 1.02/1.44 , clause( 977, [ 'c_Relation_Ototal__on'( 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), Y, X ) ] )
% 1.02/1.44 , clause( 978, [ =( 'c_Finite__Set_Ofold__image'( X, Y, Z,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), U, T ), Z ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 979, [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ] )
% 1.02/1.44 , clause( 980, [ =( 'c_Finite__Set_Ofold'( X, Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), Y ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 981, [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.02/1.44 ) ), 'tc_fun'( X, 'tc_bool' ) ) ] )
% 1.02/1.44 , clause( 982, [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.02/1.44 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 983, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.02/1.44 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ] )
% 1.02/1.44 , clause( 984, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.02/1.44 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ] )
% 1.02/1.44 , clause( 985, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.02/1.44 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ] )
% 1.02/1.44 , clause( 986, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.02/1.44 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ] )
% 1.02/1.44 , clause( 987, [ ~( =( 'c_Collect'( X, Y ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Y, 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( X, Z ) ) ) ] )
% 1.02/1.44 , clause( 988, [ ~( 'c_Wellfounded_Omax__extp'( X, Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' ) ), 't_a' ) )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 989, [ ~( 'c_Finite__Set_Ofold1Set'( X,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Z, Y ) ) ] )
% 1.02/1.44 , clause( 990, [ ~( =( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 ) ) ] )
% 1.02/1.44 , clause( 991, [ =( 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.02/1.44 ) ) ) ] )
% 1.02/1.44 , clause( 992, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), Y )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 993, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), Y ), Y )
% 1.02/1.44 ] )
% 1.02/1.44 , clause( 994, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.02/1.44 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 995, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_fun'( Y,
% 1.02/1.44 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.02/1.44 ) ] )
% 1.02/1.44 , clause( 996, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.02/1.44 'tc_bool' ) ), X ) ] )
% 1.02/1.44 , clause( 997, [ 'c_Finite__Set_Ofinite'( 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), X ) ] )
% 1.02/1.44 , clause( 998, [ =( X, Y ), ~( 'c_Finite__Set_Ofold__graph'( Z, Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), X, T, U ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 999, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 1000, [ =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), Y ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 1001, [ =( 'c_Relation_OImage'( X, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Y, 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 1002, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ] )
% 1.02/1.44 , clause( 1003, [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ) ), Y, 'tc_fun'( X, 'tc_bool' ) ) ] )
% 1.02/1.44 , clause( 1004, [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), 'c_Set_Oimage'( Y, Z, T, X ) ) ), =( Z,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 1005, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.02/1.44 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ] )
% 1.02/1.44 , clause( 1006, [ =( 'c_Set_Oimage'( X, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Y, 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 1007, [ 'c_Fun_Oinj__on'( X, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Y, 'tc_bool' ) ), Y, Z ) ] )
% 1.02/1.44 , clause( 1008, [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( Y, 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X
% 1.02/1.44 , Z ) ] )
% 1.02/1.44 , clause( 1009, [ 'c_Finite__Set_Ofold__graph'( X, Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Y, Z, T ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 1010, [ 'c_Nitpick_Ofold__graph_H'( X, Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Y, Z, T ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 1011, [ ~( =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.02/1.44 ), =( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 1012, [ ~( =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , Y ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.02/1.44 ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 1013, [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.02/1.44 ) ), 'c_Set_Oimage'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.44 'tc_bool' ) ), Z, X ) ) ] )
% 1.02/1.44 , clause( 1014, [ =( 'c_Fun_Ooverride__on'( X, Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), X ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 1015, [ =( hAPP( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( 't_a', 'tc_bool'
% 1.02/1.44 ) ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool'
% 1.02/1.44 ), 'tc_bool' ), X ) ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'(
% 1.02/1.44 't_a', 'tc_bool' ), 'tc_bool' ), Y ) ), 'v_x' ), hAPP( hAPP( 'c_in'(
% 1.02/1.44 't_a' ), 'v_x' ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( 't_a', 'tc_bool'
% 1.02/1.44 ) ), X ), Y ) ) ) ] )
% 1.02/1.44 , clause( 1016, [ =( hAPP( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( 't_a', 'tc_bool'
% 1.02/1.44 ) ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool'
% 1.02/1.44 ), 'tc_bool' ), X ) ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'(
% 1.02/1.44 't_a', 'tc_bool' ), 'tc_bool' ), Y ) ), 'v_x' ), hAPP( hAPP( 'c_in'(
% 1.02/1.44 't_a' ), 'v_x' ), hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( 't_a', 'tc_bool'
% 1.02/1.44 ) ), X ), Y ) ) ) ] )
% 1.02/1.44 , clause( 1017, [ =( hAPP( 'c_Map_Orestrict__map'( X,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' ) ), 't_a', Y
% 1.02/1.44 ), 'v_x' ), 'c_Option_Ooption_ONone'( Y ) ) ] )
% 1.02/1.44 , clause( 1018, [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, 't_a' ), 'v_x' ),
% 1.02/1.44 hAPP( X, hAPP( Y, 'v_x' ) ) ) ] )
% 1.02/1.44 , clause( 1019, [ =( hAPP( 'c_Fun_Oid'( 't_a' ), 'v_x' ), 'v_x' ) ] )
% 1.02/1.44 , clause( 1020, [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, 't_a', Z, T ), 'v_x' ),
% 1.02/1.44 hAPP( Y, hAPP( X, 'v_x' ) ) ) ] )
% 1.02/1.44 , clause( 1021, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.02/1.44 Y ), 'tc_bool' ) ), Y ) ] )
% 1.02/1.44 , clause( 1022, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, Z ), ~(
% 1.02/1.44 'c_Hoare__Mirabelle_Otriple__valid'( 'c_Suc'( X ), Y, Z ) ) ] )
% 1.02/1.44 , clause( 1023, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~(
% 1.02/1.44 hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y )
% 1.02/1.44 , Z ) ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.02/1.44 't_a' ) ), 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1'( T, X ) ), T
% 1.02/1.44 ) ), ~( 'c_Hoare__Mirabelle_Ohoare__valids'( T, Z, 't_a' ) ) ] )
% 1.02/1.44 , clause( 1024, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~(
% 1.02/1.44 hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y )
% 1.02/1.44 , Z ) ) ), ~( 'c_Hoare__Mirabelle_Otriple__valid'( 'c_Suc'( X ),
% 1.02/1.44 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1'( X, Z ), 't_a' ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 1025, [ 'c_Hoare__Mirabelle_Ohoare__valids'( X, Y, 't_a' ),
% 1.02/1.44 'c_Hoare__Mirabelle_Otriple__valid'(
% 1.02/1.44 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__2'( X, Y ), Z, 't_a' ),
% 1.02/1.44 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Z
% 1.02/1.44 ), X ) ) ) ] )
% 1.02/1.44 , clause( 1026, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~(
% 1.02/1.44 hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y )
% 1.02/1.44 , Z ) ) ), ~( 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 1.02/1.44 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1'( T, X ), 't_a' ) ), ~(
% 1.02/1.44 'c_Hoare__Mirabelle_Ohoare__valids'( T, Z, 't_a' ) ) ] )
% 1.02/1.44 , clause( 1027, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ] )
% 1.02/1.44 , clause( 1028, [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.02/1.44 'c_ATP__Linkup_Osko__Set__Xex__in__conv__1__1'( Y, X ) ), Y ) ), =( Y,
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 1.02/1.44 , clause( 1029, [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.02/1.44 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ),
% 1.02/1.44 'c_ATP__Linkup_Osko__Set__Xall__not__in__conv__1__1'( X, Y ) ), X ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 1030, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( =( hAPP( hAPP(
% 1.02/1.44 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.02/1.44 , T ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) )
% 1.02/1.44 ) ] )
% 1.02/1.44 , clause( 1031, [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.02/1.44 'tc_bool' ) ), 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y,
% 1.02/1.44 Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) ), =( hAPP( Z, U ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( T ), U ), Y ) ) ) ] )
% 1.02/1.44 , clause( 1032, [ ~( =(
% 1.02/1.44 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, Y, Z, 'tc_fun'(
% 1.02/1.44 T, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool'
% 1.02/1.44 ) ) ) ), =( hAPP( Y, U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.02/1.44 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), X ) ) ) ] )
% 1.02/1.44 , clause( 1033, [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.02/1.44 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ),
% 1.02/1.44 'c_ATP__Linkup_Osko__Set__Xequals0I__1__1'( X, Y ) ), X ) ) ] )
% 1.02/1.44 , clause( 1034, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ),
% 1.02/1.44 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.02/1.44 'tc_bool' ) ), Z ) ) ) ) ] )
% 1.02/1.44 , clause( 1035, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL(
% 1.02/1.44 hAPP( hAPP( 'c_in'( Z ), X ), Y ) ) ] )
% 1.02/1.44 , clause( 1036, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.02/1.44 =( 'c_Complete__Lattice_OSup__class_OSup'( 'c_Orderings_Obot__class_Obot'(
% 1.02/1.44 'tc_fun'( X, 'tc_bool' ) ), X ), 'c_Orderings_Obot__class_Obot'( X ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 1037, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~(
% 1.02/1.44 hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y )
% 1.02/1.44 , Z ) ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.02/1.44 't_a' ) ), 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1'( X, Z ) ),
% 1.02/1.44 Z ) ) ] )
% 1.02/1.44 , clause( 1038, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.02/1.44 , clause( 1039, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.02/1.44 , Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ]
% 1.02/1.44 )
% 1.02/1.44 , clause( 1040, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.02/1.44 , clause( 1041, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.02/1.44 , clause( 1042, [ =( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a'
% 1.02/1.44 , 'tc_bool' ) ), 'v_x' ), hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' ) ) ) ) ] )
% 1.02/1.44 , clause( 1043, [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.02/1.44 X, 'tc_bool' ) ), Y ) ) ) ] )
% 1.02/1.44 , clause( 1044, [ ~( 'class_Orderings_Obot'( X ) ), =( hAPP(
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.02/1.44 , clause( 1045, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 1.02/1.44 hAPP( Z, Y ) ) ) ] )
% 1.02/1.44 , clause( 1046, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.02/1.44 , Y ), X ) ) ) ] )
% 1.02/1.44 , clause( 1047, [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.02/1.44 Z ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) )
% 1.02/1.44 ) ] )
% 1.02/1.44 , clause( 1048, [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.02/1.44 't_a' ) ), 'v_xa' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.02/1.44 'tc_Hoare__Mirabelle_Otriple'( 't_a' ), 'tc_bool' ) ) ) ) ] )
% 1.02/1.44 , clause( 1049, [ ~( 'c_Hoare__Mirabelle_Otriple__valid'( 'v_x', 'v_xa',
% 1.02/1.44 't_a' ) ) ] )
% 1.02/1.44 , clause( 1050, [ 'c_Hoare__Mirabelle_Otriple__valid'( 'v_x', X, 't_a' ),
% 1.02/1.44 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), X
% 1.02/1.44 ), 'v_Ga' ) ) ) ] )
% 1.02/1.44 , clause( 1051, [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_fun'( X
% 1.02/1.44 , Y ) ), ~( 'class_Complete__Lattice_Ocomplete__lattice'( Y ) ) ] )
% 1.02/1.44 , clause( 1052, [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) )
% 1.02/1.44 , ~( 'class_Lattices_Olattice'( Y ) ) ] )
% 1.02/1.44 , clause( 1053, [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) )
% 1.02/1.44 , ~( 'class_Lattices_Olattice'( Y ) ) ] )
% 1.02/1.44 , clause( 1054, [ 'class_Lattices_Odistrib__lattice'( 'tc_fun'( X, Y ) ),
% 1.02/1.44 ~( 'class_Lattices_Odistrib__lattice'( Y ) ) ] )
% 1.02/1.44 , clause( 1055, [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ),
% 1.02/1.44 ~( 'class_Lattices_Obounded__lattice'( Y ) ) ] )
% 1.02/1.44 , clause( 1056, [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_fun'( X, Y ) ),
% 1.02/1.44 ~( 'class_Finite__Set_Ofinite_Ofinite'( Y ) ), ~(
% 1.02/1.44 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ] )
% 1.02/1.44 , clause( 1057, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.44 'class_Orderings_Opreorder'( Y ) ) ] )
% 1.02/1.44 , clause( 1058, [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.44 'class_Lattices_Olattice'( Y ) ) ] )
% 1.02/1.44 , clause( 1059, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.45 'class_Orderings_Oorder'( Y ) ) ] )
% 1.02/1.45 , clause( 1060, [ 'class_Orderings_Otop'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.45 'class_Orderings_Otop'( Y ) ) ] )
% 1.02/1.45 , clause( 1061, [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.45 'class_Orderings_Obot'( Y ) ) ] )
% 1.02/1.45 , clause( 1062, [ 'class_HOL_Ominus'( 'tc_fun'( X, Y ) ), ~(
% 1.02/1.45 'class_HOL_Ominus'( Y ) ) ] )
% 1.02/1.45 , clause( 1063, [ 'class_HOL_Oord'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Oord'(
% 1.02/1.45 Y ) ) ] )
% 1.02/1.45 , clause( 1064, [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ] )
% 1.02/1.45 , clause( 1065, [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ] )
% 1.02/1.45 , clause( 1066, [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ] )
% 1.02/1.45 , clause( 1067, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 1.02/1.45 , clause( 1068, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 1.02/1.45 , clause( 1069, [ 'class_Lattices_Olattice'( 'tc_nat' ) ] )
% 1.02/1.45 , clause( 1070, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 1.02/1.45 , clause( 1071, [ 'class_Orderings_Obot'( 'tc_nat' ) ] )
% 1.02/1.45 , clause( 1072, [ 'class_HOL_Ominus'( 'tc_nat' ) ] )
% 1.02/1.45 , clause( 1073, [ 'class_HOL_Oord'( 'tc_nat' ) ] )
% 1.02/1.45 , clause( 1074, [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_bool' )
% 1.02/1.45 ] )
% 1.02/1.45 , clause( 1075, [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ] )
% 1.02/1.45 , clause( 1076, [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ] )
% 1.02/1.45 , clause( 1077, [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ] )
% 1.02/1.45 , clause( 1078, [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ] )
% 1.02/1.45 , clause( 1079, [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_bool' ) ] )
% 1.02/1.45 , clause( 1080, [ 'class_Orderings_Opreorder'( 'tc_bool' ) ] )
% 1.02/1.45 , clause( 1081, [ 'class_Lattices_Olattice'( 'tc_bool' ) ] )
% 1.02/1.45 , clause( 1082, [ 'class_Orderings_Oorder'( 'tc_bool' ) ] )
% 1.02/1.45 , clause( 1083, [ 'class_Orderings_Otop'( 'tc_bool' ) ] )
% 1.02/1.45 , clause( 1084, [ 'class_Orderings_Obot'( 'tc_bool' ) ] )
% 1.02/1.45 , clause( 1085, [ 'class_HOL_Ominus'( 'tc_bool' ) ] )
% 1.02/1.45 , clause( 1086, [ 'class_HOL_Oord'( 'tc_bool' ) ] )
% 1.02/1.45 , clause( 1087, [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_Option_Ooption'(
% 1.02/1.45 X ) ), ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ] )
% 1.02/1.45 , clause( 1088, [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ] )
% 1.02/1.45 , clause( 1089, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y
% 1.02/1.45 ) ) ) ] )
% 1.02/1.45 ] ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 470, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.45 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.02/1.45 , clause( 1038, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.45 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.02/1.45 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.02/1.45 )] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 resolution(
% 1.02/1.45 clause( 1945, [] )
% 1.02/1.45 , clause( 470, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.02/1.45 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.02/1.45 , 0, clause( 1048, [ hBOOL( hAPP( hAPP( 'c_in'(
% 1.02/1.45 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), 'v_xa' ),
% 1.02/1.45 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.02/1.45 't_a' ), 'tc_bool' ) ) ) ) ] )
% 1.02/1.45 , 0, substitution( 0, [ :=( X, 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.02/1.45 :=( Y, 'v_xa' )] ), substitution( 1, [] )).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 subsumption(
% 1.02/1.45 clause( 474, [] )
% 1.02/1.45 , clause( 1945, [] )
% 1.02/1.45 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 end.
% 1.02/1.45
% 1.02/1.45 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.02/1.45
% 1.02/1.45 Memory use:
% 1.02/1.45
% 1.02/1.45 space for terms: 36865
% 1.02/1.45 space for clauses: 53184
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 clauses generated: 573
% 1.02/1.45 clauses kept: 475
% 1.02/1.45 clauses selected: 0
% 1.02/1.45 clauses deleted: 0
% 1.02/1.45 clauses inuse deleted: 0
% 1.02/1.45
% 1.02/1.45 subsentry: 5252
% 1.02/1.45 literals s-matched: 3400
% 1.02/1.45 literals matched: 3289
% 1.02/1.45 full subsumption: 1434
% 1.02/1.45
% 1.02/1.45 checksum: 29758915
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 Bliksem ended
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