%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV650-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 16:27:28 EDT 2022
% Result : Timeout 300.10s 300.63s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV650-1 : TPTP v8.1.0. Released v4.1.0.
% 0.00/0.11 % Command : bliksem %s
% 0.12/0.31 % Computer : n032.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % DateTime : Wed Jun 15 23:07:59 EDT 2022
% 0.12/0.31 % CPUTime :
% 1.19/1.61 *** allocated 10000 integers for termspace/termends
% 1.19/1.61 *** allocated 10000 integers for clauses
% 1.19/1.61 *** allocated 10000 integers for justifications
% 1.19/1.61 *** allocated 15000 integers for termspace/termends
% 1.19/1.61 *** allocated 22500 integers for termspace/termends
% 1.19/1.61 *** allocated 33750 integers for termspace/termends
% 1.19/1.61 *** allocated 50625 integers for termspace/termends
% 1.19/1.61 Bliksem 1.12
% 1.19/1.61
% 1.19/1.61
% 1.19/1.61 Automatic Strategy Selection
% 1.19/1.61
% 1.19/1.61 Clauses:
% 1.19/1.61 [
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.61 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.19/1.61 ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.61 X ), Y ), Z ) ), X ) ],
% 1.19/1.61 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), X,
% 1.19/1.61 'tc_nat' ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.19/1.61 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.19/1.61 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.61 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.61 Y, X ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Z,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.19/1.61 ) ), Z ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U )
% 1.19/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~(
% 1.19/1.61 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.19/1.61 ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.19/1.61 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.19/1.61 ],
% 1.19/1.61 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.19/1.61 'c_Set_Oimage'( Y, Z, T, X ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.19/1.61 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.19/1.61 hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.19/1.61 ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_lessequals'( Z, Y, X
% 1.19/1.61 ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.19/1.61 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z, X, X, Y ), T, hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), U ), Y, X ), ~( 'c_Lim_OLIM'( Z, T,
% 1.19/1.61 U, Y, X ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ), U
% 1.19/1.61 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.19/1.61 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.19/1.61 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.19/1.61 ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U
% 1.19/1.61 , 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ),
% 1.19/1.61 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.19/1.61 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.19/1.61 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.19/1.61 ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ),
% 1.19/1.61 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.19/1.61 ), Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 1.19/1.61 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.19/1.61 ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~(
% 1.19/1.61 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.61 , hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ), U, X
% 1.19/1.61 ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ),
% 1.19/1.61 Y ), T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.19/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.19/1.61 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 1.19/1.61 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 1.19/1.61 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.19/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.19/1.61 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Lim_OLIM'(
% 1.19/1.61 'c_COMBC'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, X, X ), Z, hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X, X ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ],
% 1.19/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X, 'tc_fun'( Y,
% 1.19/1.61 'tc_bool' ) ), X ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.19/1.61 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.19/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.61 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.19/1.61 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.19/1.61 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.19/1.61 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.19/1.61 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.19/1.61 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.19/1.61 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.19/1.61 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.19/1.61 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.19/1.61 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.61 X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.61 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.61 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.19/1.61 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ), ~(
% 1.19/1.61 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.19/1.61 ],
% 1.19/1.61 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.19/1.61 X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y )
% 1.19/1.61 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y
% 1.19/1.61 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.19/1.61 X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y )
% 1.19/1.61 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.19/1.61 X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z )
% 1.19/1.61 , 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~(
% 1.19/1.61 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 1.19/1.61 , =( X, Z ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.19/1.61 [ =( 'c_Set_Oimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.19/1.61 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.19/1.61 [ 'c_Fun_Oinj__on'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.19/1.61 'tc_bool' ) ), Y, Z ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.19/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.19/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.19/1.61 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.19/1.61 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ],
% 1.19/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.19/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.19/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.19/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.19/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~(
% 1.19/1.61 'c_lessequals'( Z, Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ),
% 1.19/1.61 'c_lessequals'( Y, Z, X ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~(
% 1.19/1.61 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.19/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, X,
% 1.19/1.61 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.19/1.61 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.61 , Y, X ) ) ],
% 1.19/1.61 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.19/1.61 X ), Y ), X, 'tc_nat' ) ],
% 1.19/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.19/1.61 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( T, X, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.19/1.61 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T,
% 1.19/1.61 Z, 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), ~( 'c_lessequals'(
% 1.19/1.61 Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.61 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.19/1.61 ), Z ), Y ), 'tc_nat' ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.61 'tc_nat' ) ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 1.19/1.61 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.19/1.61 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.61 'tc_nat' ) ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.61 , Y ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) )
% 1.19/1.61 , ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.61 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.61 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 1.19/1.61 'tc_nat' ) ],
% 1.19/1.61 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.19/1.61 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), Z ),
% 1.19/1.61 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.19/1.61 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.61 X ), T ), Y ) ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.19/1.61 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.19/1.61 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.19/1.61 ) ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.19/1.61 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.19/1.61 ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.61 , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin',
% 1.19/1.61 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin',
% 1.19/1.61 'tc_Int_Oint' ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin', 'tc_Int_Oint' ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin',
% 1.19/1.61 'tc_Int_Oint' ) ) ],
% 1.19/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.19/1.61 , Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.19/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X,
% 1.19/1.61 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( 'c_Orderings_Obot__class_Obot'(
% 1.19/1.61 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.19/1.61 Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.19/1.61 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ) ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Lim_OLIM'(
% 1.19/1.61 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_COMBC'(
% 1.19/1.61 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), X )
% 1.19/1.61 , hAPP( Y, Z ), X, X, X ), X, 'tc_fun'( X, X ), X ), 'c_COMBC'(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z, X, X, X ), X, X, X ), Z, T, X, X )
% 1.19/1.61 , ~( 'c_Deriv_Oderiv'( Y, Z, T, X ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( Y
% 1.19/1.61 , Z, T, X ), ~( 'c_Lim_OLIM'( 'c_COMBS'( 'c_COMBB'(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_COMBC'( 'c_COMBB'(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), X ), hAPP( Y,
% 1.19/1.61 Z ), X, X, X ), X, 'tc_fun'( X, X ), X ), 'c_COMBC'(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z, X, X, X ), X, X, X ), Z, T, X, X )
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.19/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.19/1.61 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.19/1.61 'c_Set_Oimage'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 1.19/1.61 ) ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.61 , hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), Y ) ),
% 1.19/1.61 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.19/1.61 ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ],
% 1.19/1.61 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, U, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), Z, T ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.19/1.61 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.19/1.61 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.19/1.61 , X ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.19/1.61 , X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.61 'tc_nat' ), X ), Y ) ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z, T ) ) ),
% 1.19/1.61 ~( 'c_Fun_Oinj__on'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.19/1.61 U, 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ), =( Y, U ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.19/1.61 ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.19/1.61 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.19/1.61 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.19/1.61 ) ],
% 1.19/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.19/1.61 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.19/1.61 ) ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( X ), Y, X ),
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'(
% 1.19/1.61 X ) ) ],
% 1.19/1.61 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 1.19/1.61 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Lim_OLIM'(
% 1.19/1.61 'c_COMBC'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, X, X ), Z, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T
% 1.19/1.61 ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.61 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.19/1.61 ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.61 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.19/1.61 , Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.19/1.61 Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.19/1.61 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.19/1.61 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.61 , Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.19/1.61 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.19/1.61 Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 T, X ) ) ],
% 1.19/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.19/1.61 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.19/1.61 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 X ), X ) ) ],
% 1.19/1.61 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.19/1.61 ~( hBOOL( hAPP( X, T ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), hAPP( 'c_Suc', T ) ),
% 1.19/1.61 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 'tc_nat' ), Z ), T ), Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.61 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( X, Y
% 1.19/1.61 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.19/1.61 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.61 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat'
% 1.19/1.61 ) ) ],
% 1.19/1.61 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.19/1.61 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 1.19/1.61 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.19/1.61 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ],
% 1.19/1.61 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL( hAPP(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 1.19/1.61 'tc_bool' ) ), Y ) ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.19/1.61 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X
% 1.19/1.61 ), Y ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.19/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.19/1.61 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.19/1.61 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.19/1.61 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.19/1.61 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, X ), 'tc_fun'( X,
% 1.19/1.61 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, T, X ) )
% 1.19/1.61 , ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.19/1.61 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), T ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.61 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.19/1.61 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), Y ), T ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.61 , Y ) ), Z ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.19/1.61 'tc_bool' ) ), X ) ],
% 1.19/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.19/1.61 X, 'tc_bool' ) ), Y ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( X ), Y, X ), Y ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.19/1.61 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~(
% 1.19/1.61 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( 'c_lessequals'(
% 1.19/1.61 Z, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.19/1.61 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, X ), 'tc_fun'( X,
% 1.19/1.61 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, T, X ) ),
% 1.19/1.61 ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.19/1.61 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.19/1.61 ) ), Y ) ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.19/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.61 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ =( 'c_Set_Oimage'( 'c_Suc', 'c_SetInterval_Oord__class_OatLeastAtMost'(
% 1.19/1.61 X, Y, 'tc_nat' ), 'tc_nat', 'tc_nat' ),
% 1.19/1.61 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( 'c_Suc', X ), hAPP(
% 1.19/1.61 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.19/1.61 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.19/1.61 'c_lessequals'( Z, Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.19/1.61 'class_RealVector_Oreal__normed__vector'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'(
% 1.19/1.61 Z, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( Y ), T, Y, Y, Y ), Y, X, Y ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( Y ), U ), T ), W, Y, X ), ~(
% 1.19/1.61 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.19/1.61 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.19/1.61 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), T ) ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.19/1.61 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.19/1.61 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.19/1.61 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.19/1.61 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.19/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.19/1.61 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( Y, Z ), ~(
% 1.19/1.61 'c_Deriv_Oderiv'( T, U, Z, X ) ), ~( 'c_Deriv_Oderiv'( T, U, Y, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( Y, X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.19/1.61 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.19/1.61 , Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.19/1.61 'class_RealVector_Oreal__normed__algebra__1'( Y ) ), =( Z, T ), ~(
% 1.19/1.61 'c_Lim_OLIM'( U, W, T, Y, X ) ), ~( 'c_Lim_OLIM'( U, W, Z, Y, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.19/1.61 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.19/1.61 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.19/1.61 ), =( Z, Y ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ), Y ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.19/1.61 hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Oabs__class_Oabs'(
% 1.19/1.61 X ), T ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.61 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.19/1.61 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.61 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.19/1.61 ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z
% 1.19/1.61 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.61 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.19/1.61 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.61 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.19/1.61 ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.19/1.61 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( U, Y, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), Z, T ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.19/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.19/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.61 , Z ), T ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ), Y ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ), Y ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ), Y ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.19/1.61 ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.61 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.19/1.61 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.61 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.19/1.61 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.19/1.61 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.19/1.61 Z ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.19/1.61 Z ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.19/1.61 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.19/1.61 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.19/1.61 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.19/1.61 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.19/1.61 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.19/1.61 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.61 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.19/1.61 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.19/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.19/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Odiv'( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.19/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ) ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.19/1.61 hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.19/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y ) ), =( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.19/1.61 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.61 , Y ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.61 X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.19/1.61 ), Y ) ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 X ) ) ), =( Y, Z ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 X ) ) ), =( Y, Z ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.61 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.61 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.61 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.19/1.61 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.19/1.61 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.19/1.61 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.19/1.61 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T )
% 1.19/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T )
% 1.19/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.19/1.61 ) ), Z ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.19/1.61 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.61 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.19/1.61 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.19/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.19/1.61 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.19/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.19/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.61 , Y ), T ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.61 , Y ), T ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), T ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), T ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.19/1.61 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.61 T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.61 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), Z, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.61 , Z ) ) ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.19/1.61 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.61 , Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.19/1.61 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.61 , Z ) ) ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.19/1.61 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.61 , Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.19/1.61 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.19/1.61 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.61 T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.19/1.61 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.19/1.61 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.19/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.61 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.19/1.61 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), Y ), T ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.19/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.19/1.61 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), T ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.61 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.19/1.61 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.19/1.61 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.19/1.61 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X
% 1.19/1.61 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.19/1.61 ), Y ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.61 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.19/1.61 ~( 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 1.19/1.61 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.19/1.61 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.19/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.19/1.61 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( T,
% 1.19/1.61 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z,
% 1.19/1.61 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.61 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.19/1.61 'tc_fun'( X, X ), X ), Z, X, X, X ), T, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), U ), Z ), X ), ~( 'c_Deriv_Oderiv'(
% 1.19/1.61 Y, T, U, X ) ) ],
% 1.19/1.61 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.61 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y,
% 1.19/1.61 'tc_nat' ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.19/1.61 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), Y ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.19/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.61 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y, X,
% 1.19/1.61 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.61 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.19/1.61 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.19/1.61 T, X ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.19/1.61 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 1.19/1.61 Y, X ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.19/1.61 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.19/1.61 'c_lessequals'( Y, T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.19/1.61 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.19/1.61 T, X ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.19/1.61 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 1.19/1.61 Y, X ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.19/1.61 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.19/1.61 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.61 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ),
% 1.19/1.61 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.61 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Orderings_Obot__class_Obot'(
% 1.19/1.61 'tc_fun'( T, 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.19/1.61 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.19/1.61 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( Z, T, U, Y, X ),
% 1.19/1.61 ~( 'c_Lim_OLIM'( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X )
% 1.19/1.61 , Z, X, 'tc_fun'( X, X ), Y ), U, Y, X, X ), T,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.19/1.61 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.19/1.61 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.19/1.61 , T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.61 'c_Lim_OLIM'( Z, U, T, Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.19/1.61 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~(
% 1.19/1.61 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.19/1.61 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.19/1.61 'c_lessequals'( Y, Z, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.61 'c_Int_OMin', X ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.19/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( Y
% 1.19/1.61 , T, X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.19/1.61 ), ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.19/1.61 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL(
% 1.19/1.61 hAPP( X, T ) ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U
% 1.19/1.61 , X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( T, U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.19/1.61 , X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( Z, Y, X
% 1.19/1.61 ), ~( 'c_lessequals'( U, T, X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( U, T, X
% 1.19/1.61 ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.19/1.61 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.19/1.61 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( X,
% 1.19/1.61 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.19/1.61 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.19/1.61 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.61 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.19/1.61 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.19/1.61 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.19/1.61 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.19/1.61 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.19/1.61 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.19/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.19/1.61 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.19/1.61 ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z
% 1.19/1.61 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) )
% 1.19/1.61 ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.61 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.19/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.61 , Z ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U )
% 1.19/1.61 , X ), ~( 'c_lessequals'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 Y, T, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.19/1.61 ],
% 1.19/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.61 X ), Y ), Z ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.19/1.61 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.19/1.61 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Z
% 1.19/1.61 , T, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.19/1.61 X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.19/1.61 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.61 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.61 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 1.19/1.61 'tc_bool' ) ), Y ) ) ) ],
% 1.19/1.61 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.19/1.61 'tc_bool' ) ), Y ) ) ) ],
% 1.19/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.19/1.61 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.61 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), T ), Z ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 X ), T ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.19/1.61 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), ~(
% 1.19/1.61 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.19/1.61 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.19/1.61 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.19/1.61 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Series_Osums'(
% 1.19/1.61 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.19/1.61 'tc_fun'( X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_Series_Osums'(
% 1.19/1.61 Y, T, X ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Series_Osums'(
% 1.19/1.61 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.19/1.61 'tc_fun'( X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_Series_Osums'(
% 1.19/1.61 Y, T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.61 'c_HOL_Oone__class_Oone'( X ) ) ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 Y, Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.61 'c_HOL_Oone__class_Oone'( X ) ) ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.61 Z, X ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.61 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.19/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), Y ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.19/1.61 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.19/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.19/1.61 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.19/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.61 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.61 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.61 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.61 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.61 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.19/1.61 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 1.19/1.61 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.61 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.61 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.61 'tc_nat' ) ), Y ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.61 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.19/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.19/1.61 [ =( 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, Z, T, U ), U, W ),
% 1.19/1.61 'c_Set_Oimage'( 'c_COMBB'( X, Y, U, W, T ), Z, T, W ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.19/1.61 'class_RealVector_Ometric__space'( Y ) ), ~(
% 1.19/1.61 'class_RealVector_Ometric__space'( Z ) ), 'c_Lim_OLIM'( 'c_COMBB'( T, U,
% 1.19/1.61 X, Y, Z ), W, hAPP( T, V0 ), Z, Y ), ~( 'c_Lim_OLIM'( U, W, V0, Z, X ) )
% 1.19/1.61 , ~( 'c_Lim_OLIM'( T, V0, hAPP( T, V0 ), X, Y ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.61 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ), X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.19/1.61 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.19/1.61 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.19/1.61 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.19/1.61 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.19/1.61 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.19/1.61 ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 X ), T ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.19/1.61 ), X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.19/1.61 ), X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.19/1.61 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.19/1.61 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.61 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.61 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.61 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.19/1.61 ), X ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.19/1.61 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.61 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.19/1.61 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~( 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~( 'c_lessequals'(
% 1.19/1.61 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.61 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.61 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.61 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.61 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.61 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.61 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.61 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.61 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.19/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.19/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.19/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.19/1.61 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.19/1.61 ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.19/1.61 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.19/1.61 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.19/1.61 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.61 X ), Y ) ), Z ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.19/1.61 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.61 , Z ) ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Lim_OLIM'(
% 1.19/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X, X ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y, hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), =( Y, Z ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), Y ), T ), Z, X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.61 Y ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.19/1.61 Y ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.19/1.61 Y ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.19/1.61 Y ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.61 Y ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.19/1.61 Y ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.19/1.61 T, X ) ), T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.61 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.19/1.61 ) ), Z ), T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, Y, X ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.19/1.61 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W, X ) ) ]
% 1.19/1.61 ,
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~(
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 1.19/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.61 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.19/1.61 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.19/1.61 ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.61 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.19/1.61 [ ~( 'class_RealVector_Oreal__field'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), W ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ), W ) ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), W ) ), U ) ) ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.19/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.19/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W
% 1.19/1.61 ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.19/1.61 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~(
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), Z ), U ) ), W ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.19/1.61 ), W, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.19/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~(
% 1.19/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.61 X ), Z ), T ) ), W ), X ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.19/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.19/1.61 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.19/1.61 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), =( Z,
% 1.19/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.61 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.19/1.61 'c_Divides_Odiv__class_Odiv'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.19/1.61 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.19/1.61 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 Z, T, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.19/1.61 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 T, Z, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 1.19/1.61 'c_lessequals'( Y, T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.19/1.61 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 1.19/1.61 'c_lessequals'( Z, T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.19/1.61 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 Z, T, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.19/1.61 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.61 T, Z, X ), X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z )
% 1.19/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.19/1.61 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.19/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.61 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z )
% 1.19/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.61 X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.19/1.61 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.19/1.61 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.19/1.61 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.19/1.61 , V0, U, V1 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.19/1.61 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.19/1.61 , V0, U, V1 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.19/1.61 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.61 X, T, U, Y, W, V0 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.61 X, T, U, Z, W, V0 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.19/1.61 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.19/1.61 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.19/1.61 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.61 T, X, U, Y, W, V0 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.61 T, X, U, Z, W, V0 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.61 T, X, U, W, Y, V0 ) ) ],
% 1.19/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.62 T, X, U, W, Z, V0 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.19/1.62 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.19/1.62 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.19/1.62 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.19/1.62 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.19/1.62 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.19/1.62 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.19/1.62 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.19/1.62 , V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.19/1.62 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.19/1.62 W, V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.19/1.62 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.19/1.62 , V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.19/1.62 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.19/1.62 W, V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.19/1.62 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.19/1.62 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.19/1.62 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.19/1.62 W, V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.19/1.62 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.19/1.62 W, V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.19/1.62 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.19/1.62 , V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.19/1.62 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.19/1.62 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.19/1.62 , V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.62 X, T, U, Y, W, V0 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.19/1.62 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.19/1.62 , V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.19/1.62 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.62 T, X, U, Y, W, V0 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.62 T, X, U, W, Y, V0 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.19/1.62 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.19/1.62 , V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.19/1.62 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.19/1.62 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.19/1.62 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.19/1.62 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.19/1.62 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.19/1.62 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ =( 'c_Set_Oimage'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.62 X, 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.19/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, 'tc_nat' ), 'tc_nat',
% 1.19/1.62 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.62 ), Y ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.62 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ), ~(
% 1.19/1.62 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) )
% 1.19/1.62 , ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.62 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ), ~(
% 1.19/1.62 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) )
% 1.19/1.62 , ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.19/1.62 , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.62 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ), 'c_HOL_Oone__class_Oone'( X
% 1.19/1.62 ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.62 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ),
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), X ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.19/1.62 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.19/1.62 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.19/1.62 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.19/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.19/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.19/1.62 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.19/1.62 X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.19/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.19/1.62 ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.19/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.19/1.62 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.19/1.62 , X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.19/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.19/1.62 Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.19/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~( 'c_lessequals'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.19/1.62 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =( hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.62 , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), =( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.19/1.62 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ), T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.19/1.62 ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.62 'tc_nat' ), X ), Y ), hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.19/1.62 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.19/1.62 hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.19/1.62 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.19/1.62 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.19/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, X ), 'tc_fun'( X,
% 1.19/1.62 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.62 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.62 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.19/1.62 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.19/1.62 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OPls', 'tc_Int_Oint' )
% 1.19/1.62 ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.62 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.19/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.62 X ), Y ), T ) ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), X ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.19/1.62 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.19/1.62 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.19/1.62 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.19/1.62 ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.19/1.62 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.62 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.19/1.62 ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.19/1.62 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.19/1.62 ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.19/1.62 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.62 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.19/1.62 ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.19/1.62 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.19/1.62 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.19/1.62 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.19/1.62 , T, Y, X, X ), U, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), T
% 1.19/1.62 ), Y, X ), ~( 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.19/1.62 ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.19/1.62 ), Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.19/1.62 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.62 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.19/1.62 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.62 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.62 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.19/1.62 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.62 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.19/1.62 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.19/1.62 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.19/1.62 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.19/1.62 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.19/1.62 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.19/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.19/1.62 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), T ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), Z ), T, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.19/1.62 ), Y ) ), Z ) ), Z ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.62 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.19/1.62 'c_lessequals'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.62 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.62 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.19/1.62 'c_lessequals'( Z, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.62 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.19/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.19/1.62 'c_lessequals'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.19/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.19/1.62 'c_lessequals'( Z, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.62 X ), Y ), Z ) ), Z ), Y ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.19/1.62 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.19/1.62 , X ) ), T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.19/1.62 ), Z ), T, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.19/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y, hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), T ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 X ), Y ), Z ) ), Z ), Y ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.62 'c_Int_OMin', X ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Z ), Y ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.62 , Y ) ), Z ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.19/1.62 Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.19/1.62 Z, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.19/1.62 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.19/1.62 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.19/1.62 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.19/1.62 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.62 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.19/1.62 X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.19/1.62 ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~(
% 1.19/1.62 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.19/1.62 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBS'(
% 1.19/1.62 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.19/1.62 , T, Y, X, X ), U, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), W ), V0
% 1.19/1.62 ), Y, X ), ~( 'c_Lim_OLIM'( T, U, V0, Y, X ) ), ~( 'c_Lim_OLIM'( Z, U, W
% 1.19/1.62 , Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.62 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.19/1.62 hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Z
% 1.19/1.62 ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.19/1.62 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.19/1.62 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.19/1.62 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.19/1.62 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_Series_Osums'( Y
% 1.19/1.62 , T, X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.19/1.62 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.19/1.62 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_Series_Osums'( Y
% 1.19/1.62 , T, X ) ) ],
% 1.19/1.62 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.19/1.62 , Y ) ) ],
% 1.19/1.62 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 'tc_nat' ) ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.19/1.62 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.62 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.19/1.62 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.19/1.62 ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.19/1.62 ), 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.19/1.62 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.19/1.62 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.19/1.62 ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.62 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ),
% 1.19/1.62 'c_Finite__Set_Osetsum'( Y, Z, T, X ) ), 'c_Finite__Set_Osetsum'(
% 1.19/1.62 'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X, X, T ), Z, T, X ), X ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.62 'c_Int_OMin', X ) ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.62 'c_Int_OMin', X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X
% 1.19/1.62 ) ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T,
% 1.19/1.62 X, X ), Z, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X
% 1.19/1.62 ) ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T,
% 1.19/1.62 X, X ), Z, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.19/1.62 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y,
% 1.19/1.62 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.62 'tc_nat' ), X ), hAPP( 'c_Suc', Y ) ), X, 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.19/1.62 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.19/1.62 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.62 X ), Y ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z
% 1.19/1.62 ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), ~(
% 1.19/1.62 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.19/1.62 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Z, X, 'tc_fun'( X, X ),
% 1.19/1.62 Y ), T, Y, X, X ), U, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), W
% 1.19/1.62 ), T ), Y, X ), ~( 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.19/1.62 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.19/1.62 X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) )
% 1.19/1.62 , hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ),
% 1.19/1.62 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ),
% 1.19/1.62 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X,
% 1.19/1.62 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ),
% 1.19/1.62 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ),
% 1.19/1.62 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X,
% 1.19/1.62 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.19/1.62 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X
% 1.19/1.62 , Y, 'tc_nat' ) ), Y ) ) ) ],
% 1.19/1.62 [ 'c_Fun_Oinj__on'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.19/1.62 , 'tc_nat', 'tc_nat', 'tc_nat' ), Y, 'tc_nat', 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.19/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y
% 1.19/1.62 , 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.19/1.62 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' )
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.19/1.62 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.19/1.62 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.19/1.62 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.19/1.62 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.19/1.62 T ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.62 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.62 'c_lessequals'( Y, hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.19/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.19/1.62 X ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.62 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), Y, X, X, X ), Z, hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), T ), X ), ~( 'c_Deriv_Oderiv'( Y, Z
% 1.19/1.62 , T, X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), ~(
% 1.19/1.62 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.19/1.62 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Z, X, 'tc_fun'( X, X ),
% 1.19/1.62 Y ), T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.62 'c_Lim_OLIM'( Z, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.62 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.19/1.62 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, X, 'tc_nat' ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.19/1.62 X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.19/1.62 X ), Y ), Z ) ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~(
% 1.19/1.62 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.62 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.19/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.19/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, X ), 'tc_fun'( X,
% 1.19/1.62 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.19/1.62 , Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.19/1.62 , Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.19/1.62 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.19/1.62 ), Y ), X ), 'tc_nat' ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X )
% 1.19/1.62 ), X ), Y ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Y ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.19/1.62 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ), X ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.19/1.62 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.19/1.62 'class_Power_Opower'( X ) ), ~( 'class_RealVector_Ometric__space'( Y ) )
% 1.19/1.62 , 'c_Lim_OLIM'( 'c_COMBC'( 'c_COMBB'( 'c_Power_Opower__class_Opower'( X )
% 1.19/1.62 , Z, X, 'tc_fun'( 'tc_nat', X ), Y ), T, Y, 'tc_nat', X ), U, hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), W ), T ), Y, X ), ~( 'c_Lim_OLIM'( Z
% 1.19/1.62 , U, W, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.19/1.62 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.19/1.62 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( X ), W ), T ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ), X ) ) ],
% 1.19/1.62 [ =( X, hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.62 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.19/1.62 , X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~(
% 1.19/1.62 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ),
% 1.19/1.62 'c_lessequals'( Y, Z, X ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~(
% 1.19/1.62 'c_lessequals'( Z, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z
% 1.19/1.62 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ), X ), ~( 'c_lessequals'( U
% 1.19/1.62 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 , U, X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.19/1.62 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), X ), ~(
% 1.19/1.62 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), ~(
% 1.19/1.62 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =( Y,
% 1.19/1.62 'c_Series_Osuminf'( Z, X ) ), ~( 'c_Series_Osums'( Z, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.19/1.62 'c_Series_Osuminf'( Y, X ), Z ), ~( 'c_Series_Osums'( Y, Z, X ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~(
% 1.19/1.62 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~(
% 1.19/1.62 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.19/1.62 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.19/1.62 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.19/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ) ), ~(
% 1.19/1.62 'c_lessequals'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), =( 'c_Orderings_Obot__class_Obot'(
% 1.19/1.62 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Y
% 1.19/1.62 , Z, X ) ), 'c_lessequals'( Y, Z, X ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OMin',
% 1.19/1.62 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.19/1.62 , T ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.19/1.62 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.19/1.62 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.19/1.62 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.62 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.19/1.62 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.62 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.19/1.62 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), Y, X, X, 'tc_nat' ), hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_Series_Osums'( Y, Z
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.62 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ), hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.19/1.62 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.19/1.62 ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.62 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.19/1.62 ), Y ), Z ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.19/1.62 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.19/1.62 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.19/1.62 'tc_bool' ) ) ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.19/1.62 ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.19/1.62 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.19/1.62 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =( hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.19/1.62 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.19/1.62 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.19/1.62 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP(
% 1.19/1.62 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.19/1.62 , X ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ),
% 1.19/1.62 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 1.19/1.62 ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.19/1.62 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 1.19/1.62 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_lessequals'( hAPP( 'c_Suc', X ), X, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 1.19/1.62 ), Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.19/1.62 X, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.19/1.62 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ),
% 1.19/1.62 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.19/1.62 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.19/1.62 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.19/1.62 , X ) ), hAPP( 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.62 'tc_nat' ), X ), Y ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.19/1.62 , U ) ), hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z
% 1.19/1.62 ), T ), U ) ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ),
% 1.19/1.62 hAPP( 'c_Suc', Z ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.19/1.62 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z )
% 1.19/1.62 ) ],
% 1.19/1.62 [ =( X, hAPP( 'c_Suc', Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.19/1.62 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.19/1.62 V0, V1 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.19/1.62 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.19/1.62 V0, V1 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.19/1.62 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.19/1.62 , V0, V1 ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.19/1.62 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.19/1.62 , V0, V1 ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.19/1.62 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.19/1.62 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP(
% 1.19/1.62 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), 'c_lessequals'( Y,
% 1.19/1.62 X, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP(
% 1.19/1.62 'c_Suc', Y ), X, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', X ), 'tc_nat' ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.19/1.62 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.19/1.62 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.19/1.62 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.19/1.62 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.19/1.62 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.19/1.62 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.19/1.62 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.19/1.62 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OPls',
% 1.19/1.62 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ) ), Y ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ) ), Y ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.19/1.62 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.19/1.62 X ), Y ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), Z ) ) ],
% 1.19/1.62 [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.19/1.62 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.19/1.62 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.19/1.62 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.19/1.62 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.19/1.62 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ =( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 'tc_nat' ), Z ), hAPP( 'c_Suc', X ) ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), Y,
% 1.19/1.62 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.19/1.62 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.19/1.62 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.19/1.62 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.62 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.19/1.62 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), X, 'tc_nat' ) ],
% 1.19/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.62 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.19/1.62 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.19/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.62 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.19/1.62 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z )
% 1.19/1.62 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ),
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X )
% 1.19/1.62 , Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ),
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.19/1.62 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.19/1.62 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' )
% 1.19/1.62 ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.19/1.62 , Y ) ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.62 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) )
% 1.19/1.62 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( 'c_Suc', Y ) )
% 1.19/1.62 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.19/1.62 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ) ), Z )
% 1.19/1.62 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X
% 1.19/1.62 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ),
% 1.19/1.62 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.19/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.19/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), U ), 'tc_nat'
% 1.19/1.62 ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.19/1.62 , T, 'tc_nat' ), 'tc_nat', X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.19/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), U
% 1.19/1.62 ), 'tc_nat' ), 'tc_nat', X ) ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.19/1.62 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.19/1.62 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( X ), T ), U ), X ), ~( 'c_Series_Osums'( Z
% 1.19/1.62 , U, X ) ), ~( 'c_Series_Osums'( Y, T, X ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.19/1.62 ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , Z ), Y ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.19/1.62 ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , X ), Y ), 'tc_nat' ) ],
% 1.19/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , Y ), X ), 'tc_nat' ) ],
% 1.19/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , X ), Y ), 'tc_nat' ) ],
% 1.19/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , X ), Y ), 'tc_nat' ) ],
% 1.19/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.19/1.62 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 X, T, 'tc_nat' ) ],
% 1.19/1.62 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.19/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.19/1.62 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.19/1.62 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.19/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.19/1.62 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.19/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.19/1.62 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ),
% 1.19/1.62 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.19/1.62 Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.19/1.62 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.62 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.19/1.62 ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.19/1.62 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.19/1.62 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.19/1.62 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.62 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ), 'tc_nat'
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.19/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z
% 1.19/1.62 ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.19/1.62 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.19/1.62 X ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.19/1.62 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y )
% 1.19/1.62 , T ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.19/1.62 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.19/1.62 , X ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OMin',
% 1.19/1.62 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X, 'tc_fun'( Y,
% 1.19/1.62 'tc_bool' ) ), X ) ],
% 1.19/1.62 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.62 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.62 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.62 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.62 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.19/1.62 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.19/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.19/1.62 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.19/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.19/1.62 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.19/1.62 , X ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.19/1.62 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.19/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.19/1.62 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.19/1.62 ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.19/1.62 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.19/1.62 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X, hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.19/1.62 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.19/1.62 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.62 'c_Int_OMin', X ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.62 ), Y ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.62 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.62 X ), Y ), Z ) ), T, X ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.62 'tc_nat' ), X ), Y ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.19/1.62 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.19/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 X, 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.62 'tc_nat' ), X ), 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), Y,
% 1.19/1.62 'tc_nat' ) ],
% 1.19/1.62 [ =( 'c_Set_Oimage'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y
% 1.19/1.62 , Z, 'tc_fun'( T, 'tc_bool' ) ), T, U ),
% 1.19/1.62 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oimage'( X, Y, T, U
% 1.19/1.62 ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.19/1.62 Y ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.19/1.62 Y ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.62 ), X ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.19/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.19/1.62 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.19/1.62 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.19/1.62 'c_lessequals'( Z, Y, X ) ],
% 1.19/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.19/1.62 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.19/1.62 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.19/1.62 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.62 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.19/1.62 X ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.62 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , 'tc_nat' ), 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.19/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , 'tc_nat' ), 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.19/1.62 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.19/1.62 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.19/1.62 , 'tc_nat' ), 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), T ) ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ) ), Y ) ), ~(
% 1.19/1.62 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.19/1.62 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.19/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.19/1.62 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ) ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.19/1.62 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.19/1.62 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 1.19/1.62 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.19/1.62 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.19/1.62 , hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.19/1.62 ) ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.19/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.19/1.62 , hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.62 'c_Suc', T ), Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.19/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.19/1.62 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ) ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.19/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.19/1.62 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.19/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.19/1.62 , T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.19/1.62 ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.19/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( 'c_Suc', Z ), T,
% 1.19/1.62 'tc_nat' ), 'tc_nat', X ) ) ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.19/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.19/1.62 , hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.19/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.19/1.62 ) ), hAPP( Y, hAPP( 'c_Suc', T ) ) ) ), 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.62 'c_Suc', T ), Z, 'tc_nat' ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.19/1.62 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.19/1.62 'tc_Int_Oint' ) ) ],
% 1.19/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.19/1.62 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'(
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ), 'tc_nat' ), 'tc_nat', X
% 1.19/1.62 ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.19/1.62 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.19/1.62 , U, 'tc_nat' ), 'tc_nat', X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.19/1.62 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.62 'c_Int_OPls' ) ), X ) ), X ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.62 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.19/1.62 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.19/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.19/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.19/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.19/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.62 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.19/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.19/1.62 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.19/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.19/1.62 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.19/1.62 'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z,
% 1.19/1.62 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat', X, 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( X ), T ), 'c_Finite__Set_Osetsum'( Y,
% 1.19/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.62 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ), X ), ~( 'c_Series_Osums'( Y,
% 1.19/1.62 T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.19/1.62 ,
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.19/1.62 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.19/1.62 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), =( Y,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), =( Z,
% 1.19/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.19/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.19/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.19/1.62 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ),
% 1.19/1.62 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.19/1.62 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ),
% 1.19/1.62 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.19/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.19/1.62 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), X ), Y ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Y ), X ) ],
% 1.19/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.19/1.62 ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ),
% 1.19/1.62 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.62 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ),
% 1.19/1.62 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T
% 1.19/1.62 ) ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.19/1.62 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.19/1.62 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U,
% 1.19/1.62 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.19/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ), U,
% 1.19/1.62 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.62 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z
% 1.19/1.62 ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.19/1.62 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.19/1.62 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ), hAPP(
% 1.19/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ), ~(
% 1.19/1.62 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.19/1.62 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ) ), U ) )
% 1.19/1.62 , ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.23/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.23/1.62 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.23/1.62 'tc_nat' ) ) ) ],
% 1.23/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.23/1.62 'tc_nat' ) ) ) ],
% 1.23/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.23/1.62 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ],
% 1.23/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.23/1.62 'c_lessequals'( T, X, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.23/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.23/1.62 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.23/1.62 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.62 ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) )
% 1.23/1.62 , 'tc_nat' ) ],
% 1.23/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.62 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T )
% 1.23/1.62 , 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.23/1.62 , Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.62 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.23/1.62 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.62 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.23/1.62 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.62 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.23/1.62 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.62 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.23/1.62 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.62 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.23/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.62 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.23/1.62 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.23/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 'tc_nat' ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.23/1.62 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.62 ), X ), X ), 'tc_nat' ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.62 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.23/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.62 ), X ), Z ), 'tc_nat' ) ) ],
% 1.23/1.62 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, hAPP( 'c_Suc', Y )
% 1.23/1.62 , 'tc_nat' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat',
% 1.23/1.62 'tc_bool' ) ) ), 'c_lessequals'( X, Y, 'tc_nat' ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.23/1.62 'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.23/1.62 'tc_nat', X, 'tc_nat' ), 'tc_nat', X, X ),
% 1.23/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.23/1.62 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( Y, Z ) ), hAPP(
% 1.23/1.62 Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ) ), ~( 'c_lessequals'( Z, T,
% 1.23/1.62 'tc_nat' ) ) ],
% 1.23/1.62 [ =( 'c_Set_Oimage'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.62 X, 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.23/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, 'tc_nat' ), 'tc_nat'
% 1.23/1.62 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.23/1.62 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.23/1.62 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.23/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( X, Y, 'tc_nat' ),
% 1.23/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), 'tc_fun'(
% 1.23/1.62 'tc_nat', 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.23/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.23/1.62 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.23/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.23/1.62 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.23/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( U, T, 'tc_nat' ), 'tc_nat'
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( U, T, 'tc_nat' ) ), ~( 'c_lessequals'( Z, U,
% 1.23/1.62 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.23/1.62 'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.23/1.62 'tc_nat', X, 'tc_nat' ), 'tc_nat', X, X ),
% 1.23/1.62 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.23/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Z, T, 'tc_nat' ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.23/1.62 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.23/1.62 'tc_fun'( X, X ), X ), Z, X, X, X ), T, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, T ) ), W ) ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Z, T ) ), hAPP( Z, T ) ) ), X )
% 1.23/1.62 , =( hAPP( Z, T ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Deriv_Oderiv'(
% 1.23/1.62 Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 'c_Finite__Set_Osetsum'(
% 1.23/1.62 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.62 X ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ),
% 1.23/1.62 'c_HOL_Oone__class_Oone'( X ) ) ) ), =( Y, 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.23/1.62 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.23/1.62 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.23/1.62 , T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_Lim_OLIM'( Z, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.23/1.62 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.23/1.62 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.23/1.62 , T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_Lim_OLIM'( Z, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.62 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.23/1.62 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.23/1.62 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.62 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.62 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ), Z ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.23/1.62 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.23/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Z ), Y ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Z ), Y ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.23/1.62 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.23/1.62 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.23/1.62 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.23/1.62 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.62 ), Y ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), =( U,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), U ), hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.62 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.23/1.62 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.62 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.23/1.62 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.62 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.23/1.62 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.23/1.62 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.23/1.62 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.23/1.62 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.23/1.62 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.23/1.62 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.23/1.62 ), T ) ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ), =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ), =( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.62 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.23/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.23/1.62 'c_COMBB'( Y, Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~(
% 1.23/1.62 'c_Deriv_Oderiv'( Y, hAPP( Z, T ), U, X ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.23/1.62 'c_COMBB'( Y, Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Y, hAPP( Z, T ), U, X ) ), ~(
% 1.23/1.62 'c_Deriv_Oderiv'( Z, T, W, X ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.23/1.62 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T, X, X, Y ), U, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), W ), Y, X ), ~( 'c_Lim_OLIM'( T,
% 1.23/1.62 U, W, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.23/1.62 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, X ), T
% 1.23/1.62 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), X ), ~(
% 1.23/1.62 'c_Deriv_Oderiv'( Z, T, U, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.62 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), =(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.23/1.62 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.23/1.62 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.23/1.62 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.62 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.23/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.62 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.62 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.23/1.62 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.23/1.62 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.23/1.62 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.23/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_Finite__Set_Osetsum'(
% 1.23/1.62 'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X, X, Z ), T, Z, X ), X ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.62 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.62 ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.23/1.62 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) )
% 1.23/1.62 ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.62 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_OPls'
% 1.23/1.62 , Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.23/1.62 ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.23/1.62 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.23/1.62 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.62 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.23/1.62 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.23/1.62 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.62 ), Y ), hAPP( 'c_Suc', Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.23/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.62 ,
% 1.23/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.23/1.62 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.23/1.62 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ),
% 1.23/1.62 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), 'c_Finite__Set_Osetsum'( Y
% 1.23/1.62 , 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), Z ), 'tc_nat' ), 'tc_nat', X
% 1.23/1.62 ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.23/1.62 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.62 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.23/1.62 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T, X, X, Y ), U,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( T, U,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.23/1.62 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( hAPP(
% 1.23/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T, X, X, Y ), U,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( T, U,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.23/1.62 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( Z,
% 1.23/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), X, Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( Z, T ), X, Y ), ~( 'c_Lim_OLIM'( Z
% 1.23/1.62 , T, hAPP( Z, T ), X, Y ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.23/1.62 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( Z, T, hAPP( Z, T
% 1.23/1.62 ), X, Y ), ~( 'c_Lim_OLIM'( 'c_COMBB'( Z, hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), X, Y, X ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( Z, T ), X, Y ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.23/1.62 'class_RealVector_Oreal__normed__vector'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'(
% 1.23/1.62 Z, hAPP( 'c_HOL_Oplus__class_Oplus'( Y ), T ), Y, X, Y ),
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( Y ), U, Y, X ), ~( 'c_Lim_OLIM'( Z, T, U, Y,
% 1.23/1.62 X ) ) ],
% 1.23/1.62 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.23/1.62 'class_RealVector_Oreal__normed__vector'( Y ) ), 'c_Lim_OLIM'( Z, T, U, Y
% 1.23/1.62 , X ), ~( 'c_Lim_OLIM'( 'c_COMBB'( Z, hAPP( 'c_HOL_Oplus__class_Oplus'( Y
% 1.23/1.62 ), T ), Y, X, Y ), 'c_HOL_Ozero__class_Ozero'( Y ), U, Y, X ) ) ],
% 1.23/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.62 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.23/1.62 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.62 ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.62 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.23/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.23/1.62 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.23/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.63 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.23/1.63 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), T ) ), =( T,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), Z ) ), =( Z,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.63 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.23/1.63 ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.23/1.63 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.23/1.63 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.23/1.63 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.23/1.63 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.23/1.63 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , X ) ), Z ) ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.23/1.63 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , X ) ), Z ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , X ) ), Z ) ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , X ) ), Z ) ), Z ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.63 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), =(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z ), =( T,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ), Y ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.23/1.63 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBS'(
% 1.23/1.63 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.23/1.63 , T, Y, X, X ), U, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), V0
% 1.23/1.63 ), Y, X ), ~( 'c_Lim_OLIM'( T, U, V0, Y, X ) ), ~( 'c_Lim_OLIM'( Z, U, W
% 1.23/1.63 , Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.23/1.63 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBS'(
% 1.23/1.63 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Z, X, 'tc_fun'( X, X ), Y ),
% 1.23/1.63 T, Y, X, X ), U, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), W ), V0 ),
% 1.23/1.63 Y, X ), ~( 'c_Lim_OLIM'( T, U, V0, Y, X ) ), ~( 'c_Lim_OLIM'( Z, U, W, Y
% 1.23/1.63 , X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.23/1.63 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.23/1.63 , X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.63 , U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'(
% 1.23/1.63 Y, T, U, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 , X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.23/1.63 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.23/1.63 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.23/1.63 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.23/1.63 ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.23/1.63 ), Z ) ), T ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.23/1.63 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.23/1.63 X ), Z, T, X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.23/1.63 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.23/1.63 X ), Z, T, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.63 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.23/1.63 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 hAPP( 'c_Suc', T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z
% 1.23/1.63 ), hAPP( 'c_Suc', T ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.23/1.63 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ) )
% 1.23/1.63 , =( Y, T ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 1.23/1.63 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.23/1.63 , Y ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.23/1.63 , Y ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X,
% 1.23/1.63 X ), U, Z, X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, U, Z, X ) ), 'c_Finite__Set_Osetsum'( T, U, Z
% 1.23/1.63 , X ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.23/1.63 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.23/1.63 , X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 'c_Series_Osums'( Z, U
% 1.23/1.63 , X ) ), ~( 'c_Series_Osums'( Y, T, X ) ) ],
% 1.23/1.63 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.63 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.63 ), X, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.63 ), X, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.63 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.23/1.63 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.63 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.23/1.63 ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', Z ), Y, 'tc_nat' ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~(
% 1.23/1.63 'class_OrderedGroup_Omonoid__mult'( X ) ), =( 'c_Finite__Set_Osetsum'(
% 1.23/1.63 'c_COMBC'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), 'c_COMBS'(
% 1.23/1.63 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), 'c_COMBB'( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.23/1.63 , 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.23/1.63 , Y ), 'tc_nat', X, X ), X, 'tc_fun'( X, X ), 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), T ), 'tc_nat', X, X ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ), 'c_Finite__Set_Osetsum'(
% 1.23/1.63 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' )
% 1.23/1.63 , 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), 'c_COMBB'(
% 1.23/1.63 hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.23/1.63 , 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.23/1.63 'tc_nat', X, X ), 'tc_nat', X, X ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ) ) ],
% 1.23/1.63 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.23/1.63 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.63 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.23/1.63 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), U ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ) ), U ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), T ), Z ) ), U ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.23/1.63 ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.23/1.63 Y ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.23/1.63 ) ), Z ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.23/1.63 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , X ) ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.23/1.63 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.23/1.63 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.23/1.63 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.23/1.63 , X ), X ), 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), Z, X, X, X )
% 1.23/1.63 , X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), U ), hAPP(
% 1.23/1.63 'c_HOL_Ouminus__class_Ouminus'( X ), W ) ), X ), ~( 'c_Deriv_Oderiv'( Z,
% 1.23/1.63 T, W, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.23/1.63 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBS'(
% 1.23/1.63 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Z, X, 'tc_fun'( X, X ), Y ),
% 1.23/1.63 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), T, X, X, Y ), Y, X, X ),
% 1.23/1.63 U, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), W ), hAPP(
% 1.23/1.63 'c_HOL_Ouminus__class_Ouminus'( X ), V0 ) ), Y, X ), ~( 'c_Lim_OLIM'( T,
% 1.23/1.63 U, V0, Y, X ) ), ~( 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ), =( Z,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.23/1.63 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.23/1.63 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.23/1.63 , ~( 'c_Series_Osums'( Z, T, X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.23/1.63 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.23/1.63 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.23/1.63 , ~( 'c_Series_Osums'( Z, T, X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.23/1.63 'tc_bool' ) ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.23/1.63 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.23/1.63 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.23/1.63 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.23/1.63 Y, X, X, Z ), T, Z, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, T, Z, X ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.23/1.63 'c_HOL_Oabs__class_Oabs'( X ), 'c_Finite__Set_Osetsum'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_Oabs__class_Oabs'( X ), Y, X, X, Z ), T, Z, X ) ),
% 1.23/1.63 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X,
% 1.23/1.63 X, Z ), T, Z, X ) ) ],
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.23/1.63 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.23/1.63 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.23/1.63 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 X, hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.23/1.63 ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.23/1.63 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.23/1.63 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.23/1.63 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.23/1.63 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.23/1.63 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.23/1.63 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X,
% 1.23/1.63 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.23/1.63 , 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.23/1.63 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.23/1.63 , 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.23/1.63 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.23/1.63 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ), Y, 'tc_nat'
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.23/1.63 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.23/1.63 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.63 , Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.63 , X, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.23/1.63 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.63 , X, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.23/1.63 ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.23/1.63 ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ), =( Y, Z ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.23/1.63 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.23/1.63 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.23/1.63 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.63 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.23/1.63 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.23/1.63 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ), 'tc_nat' ), ~( 'c_lessequals'( Y,
% 1.23/1.63 Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y )
% 1.23/1.63 , 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ),
% 1.23/1.63 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ),
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.23/1.63 , hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'(
% 1.23/1.63 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.23/1.63 ) ) ), 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', T ), Z, 'tc_nat' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.23/1.63 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.23/1.63 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.23/1.63 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.23/1.63 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat', 'tc_bool' ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( 'c_Set_Oimage'( 'c_Suc',
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( X, Y, 'tc_nat' ), 'tc_nat'
% 1.23/1.63 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc'
% 1.23/1.63 , X ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, hAPP( 'c_Suc', Y )
% 1.23/1.63 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastAtMost'( X, Y, 'tc_nat'
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 'v_m', 'tc_nat' ) ],
% 1.23/1.63 [ =( 'c_FFT__Mirabelle_ODFT'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' ),
% 1.23/1.63 'c_FFT__Mirabelle_ODFT'( X, 'c_COMBB'( Y, hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.23/1.63 ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.23/1.63 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ), Z ) ), 'c_FFT__Mirabelle_ODFT'(
% 1.23/1.63 X, 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 'tc_nat' ), hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.23/1.63 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.23/1.63 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), Z ) ) ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.23/1.63 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.23/1.63 'tc_fun'( X, X ), X ), Z, X, X, X ), T, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Y, T ) ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( Z, T ) ), hAPP( 'c_Suc', hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ), X ), =( hAPP( Z
% 1.23/1.63 , T ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Deriv_Oderiv'( Z, T, W, X
% 1.23/1.63 ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.23/1.63 [ 'c_lessequals'( 'v_m', 'v_i', 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.23/1.63 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( Z, T, U, Y, X ),
% 1.23/1.63 ~( 'c_Lim_OLIM'( W, T, U, Y, X ) ), ~( 'c_Lim_OLIM'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z, X, 'tc_fun'( X, X ), Y ), 'c_COMBB'(
% 1.23/1.63 'c_HOL_Ouminus__class_Ouminus'( X ), W, X, X, Y ), Y, X, X ), T,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), X ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.23/1.63 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), X ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.23/1.63 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.23/1.63 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.23/1.63 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.23/1.63 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.23/1.63 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.23/1.63 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.23/1.63 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.23/1.63 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, 'tc_nat' ), 'tc_nat'
% 1.23/1.63 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.23/1.63 , X ) ), ~( 'c_lessequals'( T, U, 'tc_nat' ) ), ~( 'c_lessequals'( Z, T,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'(
% 1.23/1.63 hAPP( 'c_Suc', Z ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.23/1.63 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oimage'( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'c_Set_Oimage'(
% 1.23/1.63 'c_COMBB'( 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'tc_fun'( 'tc_nat',
% 1.23/1.63 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat',
% 1.23/1.63 'tc_bool' ) ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OMin', X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.23/1.63 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.23/1.63 ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.63 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), hAPP(
% 1.23/1.63 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ), 'tc_nat' ), 'tc_nat', X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( 'c_COMBB'(
% 1.23/1.63 Y, hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', X, 'tc_nat' ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ), 'c_Finite__Set_Osetsum'(
% 1.23/1.63 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.23/1.63 ), hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.23/1.63 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.23/1.63 'tc_nat' ), 'tc_nat', X, 'tc_nat' ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.23/1.63 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBS'(
% 1.23/1.63 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.23/1.63 , T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.23/1.63 'c_Lim_OLIM'( T, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.23/1.63 'c_Lim_OLIM'( Z, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.23/1.63 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBS'(
% 1.23/1.63 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Z, X, 'tc_fun'( X, X ), Y ),
% 1.23/1.63 T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'(
% 1.23/1.63 T, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_Lim_OLIM'( Z, U,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.23/1.63 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.23/1.63 X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.63 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Y, T ) ) ), X )
% 1.23/1.63 , ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X )
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.23/1.63 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.23/1.63 X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.23/1.63 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, T ) ), U ) ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Z, T ) ) ), X )
% 1.23/1.63 , ~( 'c_Deriv_Oderiv'( Z, T, U, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, W, X )
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.23/1.63 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~( =( hAPP( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 ) ), 'c_Series_Osums'( Y, Z, X ), ~( 'c_Series_Osums'( 'c_COMBB'( Y,
% 1.23/1.63 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z, X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.23/1.63 Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), ~( 'c_Series_Osums'(
% 1.23/1.63 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z, X ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.23/1.63 , X, Z, U, W, V0 ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.23/1.63 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), Z ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.23/1.63 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 Z, T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), T,
% 1.23/1.63 'tc_nat' ), 'tc_nat', X ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, T,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.23/1.63 , X ) ), hAPP( Y, T ) ) ), 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ), 'tc_nat' ), 'tc_nat', X
% 1.23/1.63 ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.23/1.63 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 Z, U, 'tc_nat' ), 'tc_nat', X ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.23/1.63 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Y ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.23/1.63 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( Y ) ), Z ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~(
% 1.23/1.63 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ), hAPP(
% 1.23/1.63 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), 'c_Finite__Set_Osetsum'(
% 1.23/1.63 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' )
% 1.23/1.63 , 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), 'tc_nat', X, 'tc_nat' ),
% 1.23/1.63 'tc_nat', X, X ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', Z ), 'tc_nat' ),
% 1.23/1.63 'tc_nat', X ) ) ) ],
% 1.23/1.63 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ),
% 1.23/1.63 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oimage'( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'c_Set_Oimage'(
% 1.23/1.63 'c_COMBB'( 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'tc_fun'( 'tc_nat',
% 1.23/1.63 'tc_bool' ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.23/1.63 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.23/1.63 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.23/1.63 ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.23/1.63 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.23/1.63 , Y ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.63 X ), Y ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.23/1.63 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.23/1.63 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.23/1.63 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.23/1.63 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.23/1.63 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.23/1.63 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.23/1.63 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.23/1.63 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.23/1.63 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.23/1.63 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.23/1.63 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.23/1.63 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.23/1.63 [ 'c_Fun_Oinj__on'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X, 'tc_nat', 'tc_nat' ) ],
% 1.23/1.63 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.23/1.63 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.23/1.63 ) ), 'c_Complex_Oii' ) ],
% 1.23/1.63 [ =( 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.23/1.63 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), 'tc_nat',
% 1.23/1.63 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.23/1.63 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'v_a',
% 1.23/1.63 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ), 'tc_nat' ), 'tc_nat',
% 1.23/1.63 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 'tc_Complex_Ocomplex' ), 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.23/1.63 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), 'c_COMBB'(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat'
% 1.23/1.63 , 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.23/1.63 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'(
% 1.23/1.63 'v_a', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.23/1.63 ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), 'v_m', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ) ),
% 1.23/1.63 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.23/1.63 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), 'c_COMBB'(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), 'c_COMBC'(
% 1.23/1.63 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.23/1.63 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.23/1.63 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat',
% 1.23/1.63 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.23/1.63 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'(
% 1.23/1.63 'v_a', 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.23/1.63 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.23/1.63 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat',
% 1.23/1.63 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), 'v_m', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.23/1.63 ), Y ), Y ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ), =(
% 1.23/1.63 'c_Series_Osuminf'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X
% 1.23/1.63 ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'tc_nat', X, X ), X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.23/1.63 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.23/1.63 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.23/1.63 X, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.23/1.63 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.23/1.63 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.23/1.63 X ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 'tc_nat' ), 'tc_nat', X
% 1.23/1.63 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'(
% 1.23/1.63 'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T,
% 1.23/1.63 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat', X, 'tc_nat' ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ) ) ) ],
% 1.23/1.63 [ =( 'c_FFT__Mirabelle_OIDFT'( X, Y, 'v_i' ), 'c_Finite__Set_Osetsum'(
% 1.23/1.63 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'(
% 1.23/1.63 'tc_Complex_Ocomplex' ), Y, 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.23/1.63 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'(
% 1.23/1.63 hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.23/1.63 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.23/1.63 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.23/1.63 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ), =( X,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ 'c_Fun_Oinj__on'( 'c_COMBB'( 'c_Suc', hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), X,
% 1.23/1.63 'tc_nat', 'tc_nat' ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.23/1.63 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.23/1.63 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.23/1.63 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.23/1.63 ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OMin', X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat', X )
% 1.23/1.63 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( Y,
% 1.23/1.63 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( Y,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( Y,
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.23/1.63 [ ~( 'class_Power_Opower'( X ) ), ~(
% 1.23/1.63 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.23/1.63 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.23/1.63 'tc_nat', X, X ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ),
% 1.23/1.63 'tc_nat', X ), 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_COMBB'( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.23/1.63 , 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.23/1.63 , Z ), 'tc_nat', X, X ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ),
% 1.23/1.63 'tc_nat', X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~(
% 1.23/1.63 'class_OrderedGroup_Omonoid__mult'( X ) ), =( 'c_Finite__Set_Osetsum'(
% 1.23/1.63 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' )
% 1.23/1.63 , 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', T ) ), 'tc_nat'
% 1.23/1.63 , X, 'tc_nat' ), 'tc_nat', X, X ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), 'c_Finite__Set_Osetsum'(
% 1.23/1.63 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' )
% 1.23/1.63 , 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.23/1.63 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.23/1.63 'tc_nat', X, X ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ),
% 1.23/1.63 'tc_nat', X ) ) ) ],
% 1.23/1.63 [ =( 'c_FFT__Mirabelle_ODFT'( X, Y, 'v_i' ), 'c_Finite__Set_Osetsum'(
% 1.23/1.63 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex'
% 1.23/1.63 ), 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'(
% 1.23/1.63 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), 'tc_nat',
% 1.23/1.63 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.23/1.63 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), Y, 'tc_nat',
% 1.23/1.63 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.23/1.63 ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Y ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OPls', X ) ), Y ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.23/1.63 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.23/1.63 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.23/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.23/1.63 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.23/1.63 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.23/1.63 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.23/1.63 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.23/1.63 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.23/1.63 ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.63 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.23/1.63 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.23/1.63 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.23/1.63 'c_Suc', Y ) ) ) ],
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.23/1.63 ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.23/1.63 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.23/1.63 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.23/1.63 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.23/1.63 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), Y ), Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.23/1.63 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 'tc_nat' ), X ), Y ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.23/1.63 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 'tc_nat' ), X ), Y ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 hAPP( 'c_Suc', Z ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.23/1.63 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.23/1.63 , X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.23/1.63 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.23/1.63 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.23/1.63 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.63 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.23/1.63 , Z ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.23/1.63 , Z ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.63 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.23/1.63 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.63 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.23/1.63 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.23/1.63 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.23/1.63 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.23/1.63 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.63 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), Y ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.23/1.63 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.23/1.63 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.23/1.63 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.23/1.63 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.63 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.63 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.23/1.63 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.63 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.63 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.23/1.63 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.23/1.63 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.63 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.23/1.63 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.23/1.63 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.23/1.63 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.23/1.63 , Y ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.23/1.63 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.63 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.63 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.23/1.63 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.23/1.63 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.23/1.63 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), Y ), Z ) ), T ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), Y ), Z ) ), T ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.63 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.63 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.23/1.63 , W ) ) ) ],
% 1.23/1.63 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.23/1.63 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.23/1.63 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.23/1.63 , X ) ), T ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.23/1.63 ) ), =( 'c_Finite__Set_Osetsum'( Y,
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ), 'tc_nat', X ),
% 1.23/1.63 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.23/1.63 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.23/1.63 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X, X ), U, Z, X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y, U, Z, X ) )
% 1.23/1.63 , 'c_Finite__Set_Osetsum'( T, U, Z, X ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.23/1.63 ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.23/1.63 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.23/1.63 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.23/1.63 'tc_nat' ), X ), X ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.23/1.63 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.23/1.63 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.23/1.63 , Y ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.23/1.63 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 Y ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.23/1.63 Y ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 Y ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.23/1.63 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.23/1.63 Y ) ],
% 1.23/1.63 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.23/1.63 Y ) ],
% 1.23/1.63 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.23/1.63 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.23/1.63 Y ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.23/1.63 Y ) ],
% 1.23/1.63 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.23/1.63 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.23/1.63 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.23/1.63 ) ) ],
% 1.23/1.63 [ ~( =( 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.23/1.63 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), 'c_COMBB'(
% 1.23/1.63 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'v_i' ), 'c_COMBB'( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat'
% 1.23/1.63 , 'tc_nat', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.23/1.63 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.23/1.63 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( 'v_a', 'c_COMBB'( 'c_Suc'
% 1.23/1.63 , hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat'
% 1.23/1.63 , 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex',
% 1.23/1.63 'tc_Complex_Ocomplex' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.23/1.63 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'v_m', 'tc_nat' ), 'tc_nat',
% 1.23/1.63 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.23/1.63 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.23/1.63 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.23/1.63 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), 'v_i' ) ),
% 1.23/1.63 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.23/1.63 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), hAPP( hAPP(
% 1.23/1.63 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.23/1.63 'c_FFT__Mirabelle_Oroot'( 'v_m' ) ), 'v_i' ) ), 'tc_Complex_Ocomplex',
% 1.23/1.63 'tc_fun'( 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ),
% 1.23/1.63 'c_COMBB'( 'v_a', 'c_COMBB'( 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.23/1.63 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.23/1.63 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat',
% 1.23/1.63 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat',
% 1.23/1.63 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.23/1.63 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.23/1.63 'tc_nat' ), 'v_m', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ) ) ) ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.63 'class_Lattices_Olattice'( Y ) ) ],
% 1.23/1.63 [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.63 'class_Lattices_Olattice'( Y ) ) ],
% 1.23/1.63 [ 'class_Lattices_Odistrib__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.63 'class_Lattices_Odistrib__lattice'( Y ) ) ],
% 1.23/1.63 [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.63 'class_Lattices_Obounded__lattice'( Y ) ) ],
% 1.23/1.63 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.63 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.23/1.63 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.63 'class_Orderings_Opreorder'( Y ) ) ],
% 1.23/1.63 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.63 'class_Lattices_Olattice'( Y ) ) ],
% 1.23/1.63 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.23/1.63 'class_Orderings_Oorder'( Y ) ) ],
% 1.23/1.63 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 1.23/1.63 Y ) ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.23/1.63 ],
% 1.23/1.63 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.23/1.63 ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.23/1.63 ],
% 1.23/1.63 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.23/1.63 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Lattices_Oboolean__algebra'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.23/1.63 'tc_Int_Oint' ) ],
% 1.23/1.63 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.23/1.63 'tc_Int_Oint' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.23/1.63 'tc_Int_Oint' ) ],
% 1.23/1.63 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.23/1.63 ],
% 1.23/1.63 [ 'class_OrderedGroup_Olordered__ab__group__add__meet'( 'tc_Int_Oint' )
% 1.23/1.63 ],
% 1.23/1.63 [ 'class_OrderedGroup_Olordered__ab__group__add__join'( 'tc_Int_Oint' )
% 1.23/1.63 ],
% 1.23/1.63 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.23/1.63 ],
% 1.23/1.63 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.23/1.63 ,
% 1.23/1.63 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Lattices_Oupper__semilattice'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Lattices_Olower__semilattice'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Lattices_Odistrib__lattice'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Lattices_Olattice'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.23/1.64 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.23/1.64 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.23/1.64 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.23/1.64 ],
% 1.23/1.64 [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_Complex_Ocomplex' )
% 1.23/1.64 ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.23/1.64 ],
% 1.23/1.64 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.23/1.64 ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Complex_Ocomplex' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_RealVector_Oreal__normed__vector'( 'tc_Complex_Ocomplex' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_RealVector_Ometric__space'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.23/1.64 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.23/1.64 , W ) ) ) ],
% 1.23/1.64 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.23/1.64 ,
% 1.23/1.64 [ 'c_fequal'( X, X, Y ) ],
% 1.23/1.64 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.23/1.64 ] .
% 1.23/1.64
% 1.23/1.64
% 1.23/1.64 percentage equality = 0.239100, percentage horn = 0.864552
% 1.23/1.64 This is a problem with some equality
% 1.23/1.64
% 1.23/1.64
% 1.23/1.64
% 1.23/1.64 Options Used:
% 1.23/1.64
% 1.23/1.64 useres = 1
% 1.23/1.64 useparamod = 1
% 1.23/1.64 useeqrefl = 1
% 1.23/1.64 useeqfact = 1
% 1.23/1.64 usefactor = 1
% 1.23/1.64 usesimpsplitting = 0
% 1.23/1.64 usesimpdemod = 5
% 1.23/1.64 usesimpres = 3
% 1.23/1.64
% 1.23/1.64 resimpinuse = 1000
% 1.23/1.64 resimpclauses = 20000
% 1.23/1.64 substype = eqrewr
% 1.23/1.64 backwardsubs = 1
% 1.23/1.64 selectoldest = 5
% 1.23/1.64
% 1.23/1.64 litorderings [0] = split
% 1.23/1.64 litorderings [1] = extend the termordering, first sorting on arguments
% 1.23/1.64
% 1.23/1.64 termordering = kbo
% 1.23/1.64
% 1.23/1.64 litapriori = 0
% 1.23/1.64 termapriori = 1
% 1.23/1.64 litaposteriori = 0
% 1.23/1.64 termaposteriori = 0
% 1.23/1.64 demodaposteriori = 0
% 1.23/1.64 ordereqreflfact = 0
% 1.23/1.64
% 1.23/1.64 litselect = negord
% 1.23/1.64
% 1.23/1.64 maxweight = 15
% 1.23/1.64 maxdepth = 30000
% 1.23/1.64 maxlength = 115
% 1.23/1.64 maxnrvars = 195
% 1.23/1.64 excuselevel = 1
% 1.23/1.64 increasemaxweight = 1
% 1.23/1.64
% 1.23/1.64 maxselected = 10000000
% 1.23/1.64 maxnrclauses = 10000000
% 1.23/1.64
% 1.23/1.64 showgenerated = 0
% 1.23/1.64 showkept = 0
% 1.23/1.64 showselected = 0
% 1.23/1.64 showdeleted = 0
% 1.23/1.64 showresimp = 1
% 1.23/1.64 showstatus = 2000
% 1.23/1.64
% 1.23/1.64 prologoutput = 1
% 1.23/1.64 nrgoals = 5000000
% 1.23/1.64 totalproof = 1
% 1.23/1.64
% 1.23/1.64 Symbols occurring in the translation:
% 1.23/1.64
% 1.23/1.64 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.23/1.64 . [1, 2] (w:1, o:183, a:1, s:1, b:0),
% 1.23/1.64 ! [4, 1] (w:0, o:87, a:1, s:1, b:0),
% 1.23/1.64 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.23/1.64 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.23/1.64 'class_OrderedGroup_Opordered__ab__group__add__abs' [40, 1] (w:1, o:
% 1.23/1.64 93, a:1, s:1, b:0),
% 1.23/1.64 'c_HOL_Oabs__class_Oabs' [41, 1] (w:1, o:94, a:1, s:1, b:0),
% 1.23/1.64 'c_HOL_Ominus__class_Ominus' [42, 1] (w:1, o:95, a:1, s:1, b:0),
% 1.23/1.64 hAPP [44, 2] (w:1, o:208, a:1, s:1, b:0),
% 1.23/1.64 'c_lessequals' [46, 3] (w:1, o:213, a:1, s:1, b:0),
% 1.23/1.64 'tc_nat' [49, 0] (w:1, o:22, a:1, s:1, b:0),
% 1.23/1.64 'c_Divides_Odiv__class_Odiv' [50, 3] (w:1, o:214, a:1, s:1, b:0),
% 1.23/1.64 'class_OrderedGroup_Opordered__ab__group__add' [51, 1] (w:1, o:96, a:
% 1.23/1.64 1, s:1, b:0),
% 1.23/1.64 'c_HOL_Ozero__class_Ozero' [52, 1] (w:1, o:97, a:1, s:1, b:0),
% 1.23/1.64 'c_HOL_Oord__class_Oless' [53, 3] (w:1, o:215, a:1, s:1, b:0),
% 1.23/1.64 'c_HOL_Ouminus__class_Ouminus' [54, 1] (w:1, o:99, a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Oordered__idom' [55, 1] (w:1, o:102, a:1, s:1
% 1.23/1.64 , b:0),
% 1.23/1.64 'class_Int_Onumber__ring' [56, 1] (w:1, o:103, a:1, s:1, b:0),
% 1.23/1.64 'c_Int_Onumber__class_Onumber__of' [58, 2] (w:1, o:209, a:1, s:1, b:0
% 1.23/1.64 ),
% 1.23/1.64 'class_Ring__and__Field_Ofield' [59, 1] (w:1, o:104, a:1, s:1, b:0),
% 1.23/1.64
% 1.23/1.64 'c_HOL_Oinverse__class_Odivide' [60, 1] (w:1, o:105, a:1, s:1, b:0),
% 1.23/1.64
% 1.23/1.64 'class_Ring__and__Field_Odivision__by__zero' [61, 1] (w:1, o:111, a:1
% 1.23/1.64 , s:1, b:0),
% 1.23/1.64 'c_HOL_Oone__class_Oone' [62, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.23/1.64 'c_Power_Opower__class_Opower' [63, 1] (w:1, o:114, a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Oordered__field' [64, 1] (w:1, o:115, a:1, s:
% 1.23/1.64 1, b:0),
% 1.23/1.64 'c_HOL_Otimes__class_Otimes' [69, 1] (w:1, o:98, a:1, s:1, b:0),
% 1.23/1.64 'tc_bool' [70, 0] (w:1, o:36, a:1, s:1, b:0),
% 1.23/1.64 'tc_fun' [71, 2] (w:1, o:210, a:1, s:1, b:0),
% 1.23/1.64 'c_Orderings_Obot__class_Obot' [72, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.23/1.64 'c_Set_Oimage' [76, 4] (w:1, o:226, a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Olordered__ring' [77, 1] (w:1, o:116, a:1, s:
% 1.23/1.64 1, b:0),
% 1.23/1.64 'class_RealVector_Oreal__normed__vector' [78, 1] (w:1, o:117, a:1, s:
% 1.23/1.64 1, b:0),
% 1.23/1.64 'class_RealVector_Ometric__space' [79, 1] (w:1, o:118, a:1, s:1, b:0)
% 1.23/1.64 ,
% 1.23/1.64 'c_COMBB' [80, 5] (w:1, o:230, a:1, s:1, b:0),
% 1.23/1.64 'c_Lim_OLIM' [82, 5] (w:1, o:231, a:1, s:1, b:0),
% 1.23/1.64 'c_HOL_Oplus__class_Oplus' [83, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.23/1.64 'class_Orderings_Obot' [88, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.23/1.64 'class_Lattices_Odistrib__lattice' [90, 1] (w:1, o:121, a:1, s:1, b:0
% 1.23/1.64 ),
% 1.23/1.64 'c_Lattices_Oupper__semilattice__class_Osup' [91, 3] (w:1, o:216, a:1
% 1.23/1.64 , s:1, b:0),
% 1.23/1.64 'c_Lattices_Olower__semilattice__class_Oinf' [92, 3] (w:1, o:217, a:1
% 1.23/1.64 , s:1, b:0),
% 1.23/1.64 'class_RealVector_Oreal__normed__field' [95, 1] (w:1, o:122, a:1, s:1
% 1.23/1.64 , b:0),
% 1.23/1.64 'c_COMBC' [96, 5] (w:1, o:232, a:1, s:1, b:0),
% 1.23/1.64 'class_Lattices_Oupper__semilattice' [97, 1] (w:1, o:123, a:1, s:1
% 1.23/1.64 , b:0),
% 1.23/1.64 'class_Orderings_Oorder' [98, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.23/1.64 'class_Orderings_Opreorder' [99, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.23/1.64 'class_Orderings_Olinorder' [104, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.23/1.64 'class_OrderedGroup_Oab__group__add' [106, 1] (w:1, o:127, a:1, s:1
% 1.23/1.64 , b:0),
% 1.23/1.64 'class_Lattices_Oboolean__algebra' [110, 1] (w:1, o:128, a:1, s:1, b:
% 1.23/1.64 0),
% 1.23/1.64 'c_Fun_Oinj__on' [111, 4] (w:1, o:227, a:1, s:1, b:0),
% 1.23/1.64 'class_Lattices_Olattice' [112, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.23/1.64 'c_Parity_Oeven__odd__class_Oeven' [113, 2] (w:1, o:211, a:1, s:1, b:
% 1.23/1.64 0),
% 1.23/1.64 'class_Lattices_Olower__semilattice' [114, 1] (w:1, o:130, a:1, s:1
% 1.23/1.64 , b:0),
% 1.23/1.64 'c_Int_OMin' [115, 0] (w:1, o:56, a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Oordered__semidom' [116, 1] (w:1, o:132, a:1
% 1.23/1.64 , s:1, b:0),
% 1.23/1.64 'c_Divides_Odiv__class_Omod' [117, 3] (w:1, o:218, a:1, s:1, b:0),
% 1.23/1.64 'class_Lattices_Obounded__lattice' [119, 1] (w:1, o:133, a:1, s:1, b:
% 1.23/1.64 0),
% 1.23/1.64 'c_Int_OBit1' [120, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.23/1.64 'tc_Int_Oint' [121, 0] (w:1, o:60, a:1, s:1, b:0),
% 1.23/1.64 'class_OrderedGroup_Olordered__ab__group__add' [122, 1] (w:1, o:136
% 1.23/1.64 , a:1, s:1, b:0),
% 1.23/1.64 'c_SetInterval_Oord__class_OatLeastLessThan' [123, 3] (w:1, o:219, a:
% 1.23/1.64 1, s:1, b:0),
% 1.23/1.64 'c_COMBS' [124, 5] (w:1, o:233, a:1, s:1, b:0),
% 1.23/1.64 'c_Deriv_Oderiv' [126, 4] (w:1, o:228, a:1, s:1, b:0),
% 1.23/1.64 'class_OrderedGroup_Ogroup__add' [127, 1] (w:1, o:137, a:1, s:1, b:0)
% 1.23/1.64 ,
% 1.23/1.64 'c_Suc' [128, 0] (w:1, o:62, a:1, s:1, b:0),
% 1.23/1.64 'class_RealVector_Oreal__normed__algebra' [129, 1] (w:1, o:138, a:1
% 1.23/1.64 , s:1, b:0),
% 1.23/1.64 'class_OrderedGroup_Olordered__ab__group__add__abs' [130, 1] (w:1, o:
% 1.23/1.64 139, a:1, s:1, b:0),
% 1.23/1.64 'class_Ring__and__Field_Oabs__if' [131, 1] (w:1, o:140, a:1, s:1, b:0
% 1.23/1.64 ),
% 1.23/1.64 hBOOL [132, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.23/1.64 'c_SetInterval_Oord__class_OatLeastAtMost' [134, 3] (w:1, o:220, a:1
% 1.23/1.64 , s:1, b:0),
% 4.06/4.45 'class_RealVector_Oreal__normed__algebra__1' [136, 1] (w:1, o:142, a:
% 4.06/4.45 1, s:1, b:0),
% 4.06/4.45 'class_Int_Onumber' [138, 1] (w:1, o:143, a:1, s:1, b:0),
% 4.06/4.45 'class_Divides_Osemiring__div' [139, 1] (w:1, o:145, a:1, s:1, b:0),
% 4.06/4.45
% 4.06/4.45 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [140, 1]
% 4.06/4.45 (w:1, o:146, a:1, s:1, b:0),
% 4.06/4.45 'c_Int_OPls' [141, 0] (w:1, o:67, a:1, s:1, b:0),
% 4.06/4.45 'c_Int_OBit0' [142, 1] (w:1, o:134, a:1, s:1, b:0),
% 4.06/4.45 'class_OrderedGroup_Oordered__ab__group__add' [143, 1] (w:1, o:92, a:
% 4.06/4.45 1, s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Ozero__neq__one' [144, 1] (w:1, o:147, a:1
% 4.06/4.45 , s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Oidom' [145, 1] (w:1, o:148, a:1, s:1, b:0),
% 4.06/4.45
% 4.06/4.45 'class_Ring__and__Field_Oordered__semiring__strict' [146, 1] (w:1, o:
% 4.06/4.45 149, a:1, s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Opordered__ring__abs' [147, 1] (w:1, o:152
% 4.06/4.45 , a:1, s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Oordered__semiring' [148, 1] (w:1, o:150, a:1
% 4.06/4.45 , s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Oordered__ring__strict' [149, 1] (w:1, o:131
% 4.06/4.45 , a:1, s:1, b:0),
% 4.06/4.45 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [150, 1]
% 4.06/4.45 (w:1, o:153, a:1, s:1, b:0),
% 4.06/4.45 'class_OrderedGroup_Ocomm__monoid__add' [151, 1] (w:1, o:154, a:1, s:
% 4.06/4.45 1, b:0),
% 4.06/4.45 'class_Divides_Oring__div' [152, 1] (w:1, o:144, a:1, s:1, b:0),
% 4.06/4.45 'c_Series_Osums' [153, 3] (w:1, o:221, a:1, s:1, b:0),
% 4.06/4.45 'class_OrderedGroup_Opordered__comm__monoid__add' [157, 1] (w:1, o:
% 4.06/4.45 155, a:1, s:1, b:0),
% 4.06/4.45 'c_Power_Opower_Opower' [158, 3] (w:1, o:222, a:1, s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Oring' [160, 1] (w:1, o:156, a:1, s:1, b:0),
% 4.06/4.45
% 4.06/4.45 'class_OrderedGroup_Omonoid__mult' [163, 1] (w:1, o:159, a:1, s:1, b:
% 4.06/4.45 0),
% 4.06/4.45 'class_OrderedGroup_Ocomm__monoid__mult' [164, 1] (w:1, o:160, a:1
% 4.06/4.45 , s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Ocomm__semiring__1' [165, 1] (w:1, o:109, a:1
% 4.06/4.45 , s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Opordered__ring' [166, 1] (w:1, o:161, a:1
% 4.06/4.45 , s:1, b:0),
% 4.06/4.45 'class_RealVector_Oreal__field' [168, 1] (w:1, o:162, a:1, s:1, b:0)
% 4.06/4.45 ,
% 4.06/4.45 'c_Groebner__Basis_Ogb__semiring' [175, 6] (w:1, o:234, a:1, s:1, b:0
% 4.06/4.45 ),
% 4.06/4.45 'class_Ring__and__Field_Ocomm__ring__1' [181, 1] (w:1, o:106, a:1, s:
% 4.06/4.45 1, b:0),
% 4.06/4.45 'class_OrderedGroup_Opordered__ab__semigroup__add' [183, 1] (w:1, o:
% 4.06/4.45 163, a:1, s:1, b:0),
% 4.06/4.45 'class_OrderedGroup_Olordered__ab__group__add__meet' [184, 1] (w:1
% 4.06/4.45 , o:157, a:1, s:1, b:0),
% 4.06/4.45 'class_OrderedGroup_Olordered__ab__group__add__join' [185, 1] (w:1
% 4.06/4.45 , o:158, a:1, s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Oring__1' [186, 1] (w:1, o:164, a:1, s:1, b:0
% 4.06/4.45 ),
% 4.06/4.45 'class_Power_Opower' [187, 1] (w:1, o:171, a:1, s:1, b:0),
% 4.06/4.45 'c_Finite__Set_Osetsum' [190, 4] (w:1, o:229, a:1, s:1, b:0),
% 4.06/4.45 'c_Series_Osuminf' [192, 2] (w:1, o:212, a:1, s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Oordered__comm__semiring__strict' [197, 1]
% 4.06/4.45 (w:1, o:151, a:1, s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Omult__mono1' [198, 1] (w:1, o:172, a:1, s:1
% 4.06/4.45 , b:0),
% 4.06/4.45 'class_Ring__and__Field_Omult__mono' [199, 1] (w:1, o:173, a:1, s:1
% 4.06/4.45 , b:0),
% 4.06/4.45 'class_Ring__and__Field_Opordered__cancel__semiring' [200, 1] (w:1
% 4.06/4.45 , o:174, a:1, s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Opordered__semiring' [201, 1] (w:1, o:175, a:
% 4.06/4.45 1, s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Osemiring__0' [204, 1] (w:1, o:178, a:1, s:1
% 4.06/4.45 , b:0),
% 4.06/4.45 'class_Ring__and__Field_Ocomm__ring' [205, 1] (w:1, o:107, a:1, s:1
% 4.06/4.45 , b:0),
% 4.06/4.45 'v_m' [207, 0] (w:1, o:80, a:1, s:1, b:0),
% 4.06/4.45 'c_FFT__Mirabelle_ODFT' [208, 3] (w:1, o:223, a:1, s:1, b:0),
% 4.06/4.45 'tc_Complex_Ocomplex' [209, 0] (w:1, o:81, a:1, s:1, b:0),
% 4.06/4.45 'c_FFT__Mirabelle_Oroot' [210, 1] (w:1, o:179, a:1, s:1, b:0),
% 4.06/4.45 'v_i' [211, 0] (w:1, o:82, a:1, s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Osemiring__1' [212, 1] (w:1, o:180, a:1, s:1
% 4.06/4.45 , b:0),
% 4.06/4.45 'c_Complex_Oii' [213, 0] (w:1, o:83, a:1, s:1, b:0),
% 4.06/4.45 'v_a' [214, 0] (w:1, o:84, a:1, s:1, b:0),
% 4.06/4.45 'c_FFT__Mirabelle_OIDFT' [215, 3] (w:1, o:224, a:1, s:1, b:0),
% 4.06/4.45 'class_Ring__and__Field_Ocomm__semiring__0' [216, 1] (w:1, o:108, a:1
% 19.23/19.62 , s:1, b:0),
% 19.23/19.62 'class_OrderedGroup_Oab__semigroup__idem__mult' [217, 1] (w:1, o:165
% 19.23/19.62 , a:1, s:1, b:0),
% 19.23/19.62 'class_OrderedGroup_Oab__semigroup__mult' [218, 1] (w:1, o:166, a:1
% 19.23/19.62 , s:1, b:0),
% 19.23/19.62 'class_Ring__and__Field_Ocomm__semiring' [219, 1] (w:1, o:110, a:1
% 19.23/19.62 , s:1, b:0),
% 19.23/19.62 'class_OrderedGroup_Ocancel__ab__semigroup__add' [220, 1] (w:1, o:167
% 19.23/19.62 , a:1, s:1, b:0),
% 19.23/19.62 'class_OrderedGroup_Ocancel__semigroup__add' [221, 1] (w:1, o:168, a:
% 19.23/19.62 1, s:1, b:0),
% 19.23/19.62 'class_Ring__and__Field_Ono__zero__divisors' [224, 1] (w:1, o:101, a:
% 19.23/19.62 1, s:1, b:0),
% 19.23/19.62 'class_Ring__and__Field_Omult__zero' [225, 1] (w:1, o:100, a:1, s:1
% 19.23/19.62 , b:0),
% 19.23/19.62 'class_Ring__and__Field_Oring__no__zero__divisors' [226, 1] (w:1, o:
% 19.23/19.62 176, a:1, s:1, b:0),
% 19.23/19.62 'class_Ring__and__Field_Osemiring' [227, 1] (w:1, o:181, a:1, s:1, b:
% 19.23/19.62 0),
% 19.23/19.62 'class_Ring__and__Field_Oring__1__no__zero__divisors' [228, 1] (w:1
% 19.23/19.62 , o:177, a:1, s:1, b:0),
% 19.23/19.62 'class_OrderedGroup_Oab__semigroup__add' [229, 1] (w:1, o:169, a:1
% 19.23/19.62 , s:1, b:0),
% 19.23/19.62 'class_Int_Oring__char__0' [230, 1] (w:1, o:182, a:1, s:1, b:0),
% 19.23/19.62 'class_OrderedGroup_Omonoid__add' [231, 1] (w:1, o:170, a:1, s:1, b:0
% 19.23/19.62 ),
% 19.23/19.62 'c_fequal' [234, 3] (w:1, o:225, a:1, s:1, b:0).
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Starting Search:
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 2973
% 19.23/19.62 Kept: 2019
% 19.23/19.62 Inuse: 90
% 19.23/19.62 Deleted: 1
% 19.23/19.62 Deletedinuse: 0
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 10431
% 19.23/19.62 Kept: 4040
% 19.23/19.62 Inuse: 304
% 19.23/19.62 Deleted: 7
% 19.23/19.62 Deletedinuse: 0
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 16042
% 19.23/19.62 Kept: 6070
% 19.23/19.62 Inuse: 421
% 19.23/19.62 Deleted: 10
% 19.23/19.62 Deletedinuse: 0
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 20474
% 19.23/19.62 Kept: 8116
% 19.23/19.62 Inuse: 441
% 19.23/19.62 Deleted: 10
% 19.23/19.62 Deletedinuse: 0
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 27892
% 19.23/19.62 Kept: 11287
% 19.23/19.62 Inuse: 521
% 19.23/19.62 Deleted: 13
% 19.23/19.62 Deletedinuse: 0
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 36092
% 19.23/19.62 Kept: 13930
% 19.23/19.62 Inuse: 597
% 19.23/19.62 Deleted: 14
% 19.23/19.62 Deletedinuse: 0
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 41402
% 19.23/19.62 Kept: 15969
% 19.23/19.62 Inuse: 700
% 19.23/19.62 Deleted: 16
% 19.23/19.62 Deletedinuse: 0
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 48077
% 19.23/19.62 Kept: 18019
% 19.23/19.62 Inuse: 814
% 19.23/19.62 Deleted: 17
% 19.23/19.62 Deletedinuse: 0
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 53644
% 19.23/19.62 Kept: 20319
% 19.23/19.62 Inuse: 839
% 19.23/19.62 Deleted: 17
% 19.23/19.62 Deletedinuse: 0
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62 Resimplifying clauses:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 61810
% 19.23/19.62 Kept: 22444
% 19.23/19.62 Inuse: 889
% 19.23/19.62 Deleted: 346
% 19.23/19.62 Deletedinuse: 1
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 73375
% 19.23/19.62 Kept: 24672
% 19.23/19.62 Inuse: 899
% 19.23/19.62 Deleted: 346
% 19.23/19.62 Deletedinuse: 1
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 85594
% 19.23/19.62 Kept: 27445
% 19.23/19.62 Inuse: 909
% 19.23/19.62 Deleted: 346
% 19.23/19.62 Deletedinuse: 1
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 97496
% 19.23/19.62 Kept: 29990
% 19.23/19.62 Inuse: 919
% 19.23/19.62 Deleted: 346
% 19.23/19.62 Deletedinuse: 1
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 110401
% 19.23/19.62 Kept: 32603
% 19.23/19.62 Inuse: 929
% 19.23/19.62 Deleted: 346
% 19.23/19.62 Deletedinuse: 1
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 121139
% 19.23/19.62 Kept: 34762
% 19.23/19.62 Inuse: 959
% 19.23/19.62 Deleted: 346
% 19.23/19.62 Deletedinuse: 1
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 130903
% 19.23/19.62 Kept: 36883
% 19.23/19.62 Inuse: 999
% 19.23/19.62 Deleted: 346
% 19.23/19.62 Deletedinuse: 1
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62 Resimplifying inuse:
% 19.23/19.62 Done
% 19.23/19.62
% 19.23/19.62
% 19.23/19.62 Intermediate Status:
% 19.23/19.62 Generated: 140213
% 19.23/19.62 Kept: 38903
% 19.23/19.62 Inuse: 1042
% 19.23/19.62 Deleted: 346
% 19.23/19.62 Deletedinuse: 1
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 149302
% 54.48/54.87 Kept: 41524
% 54.48/54.87 Inuse: 1069
% 54.48/54.87 Deleted: 346
% 54.48/54.87 Deletedinuse: 1
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying clauses:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 156173
% 54.48/54.87 Kept: 43903
% 54.48/54.87 Inuse: 1099
% 54.48/54.87 Deleted: 707
% 54.48/54.87 Deletedinuse: 1
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 163470
% 54.48/54.87 Kept: 45912
% 54.48/54.87 Inuse: 1126
% 54.48/54.87 Deleted: 707
% 54.48/54.87 Deletedinuse: 1
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 172924
% 54.48/54.87 Kept: 48701
% 54.48/54.87 Inuse: 1149
% 54.48/54.87 Deleted: 707
% 54.48/54.87 Deletedinuse: 1
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 179618
% 54.48/54.87 Kept: 51152
% 54.48/54.87 Inuse: 1154
% 54.48/54.87 Deleted: 708
% 54.48/54.87 Deletedinuse: 2
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 186383
% 54.48/54.87 Kept: 53371
% 54.48/54.87 Inuse: 1159
% 54.48/54.87 Deleted: 708
% 54.48/54.87 Deletedinuse: 2
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 197470
% 54.48/54.87 Kept: 55560
% 54.48/54.87 Inuse: 1188
% 54.48/54.87 Deleted: 709
% 54.48/54.87 Deletedinuse: 2
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 202177
% 54.48/54.87 Kept: 58144
% 54.48/54.87 Inuse: 1194
% 54.48/54.87 Deleted: 723
% 54.48/54.87 Deletedinuse: 16
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 208600
% 54.48/54.87 Kept: 60156
% 54.48/54.87 Inuse: 1213
% 54.48/54.87 Deleted: 723
% 54.48/54.87 Deletedinuse: 16
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying clauses:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 215790
% 54.48/54.87 Kept: 62276
% 54.48/54.87 Inuse: 1233
% 54.48/54.87 Deleted: 1229
% 54.48/54.87 Deletedinuse: 16
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 225757
% 54.48/54.87 Kept: 64519
% 54.48/54.87 Inuse: 1258
% 54.48/54.87 Deleted: 1229
% 54.48/54.87 Deletedinuse: 16
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 245941
% 54.48/54.87 Kept: 68112
% 54.48/54.87 Inuse: 1268
% 54.48/54.87 Deleted: 1229
% 54.48/54.87 Deletedinuse: 16
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 253252
% 54.48/54.87 Kept: 70282
% 54.48/54.87 Inuse: 1288
% 54.48/54.87 Deleted: 1229
% 54.48/54.87 Deletedinuse: 16
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 261225
% 54.48/54.87 Kept: 72289
% 54.48/54.87 Inuse: 1312
% 54.48/54.87 Deleted: 1229
% 54.48/54.87 Deletedinuse: 16
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 268530
% 54.48/54.87 Kept: 74485
% 54.48/54.87 Inuse: 1333
% 54.48/54.87 Deleted: 1229
% 54.48/54.87 Deletedinuse: 16
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 276286
% 54.48/54.87 Kept: 76528
% 54.48/54.87 Inuse: 1353
% 54.48/54.87 Deleted: 1229
% 54.48/54.87 Deletedinuse: 16
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 285124
% 54.48/54.87 Kept: 78885
% 54.48/54.87 Inuse: 1378
% 54.48/54.87 Deleted: 1229
% 54.48/54.87 Deletedinuse: 16
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 293578
% 54.48/54.87 Kept: 80894
% 54.48/54.87 Inuse: 1414
% 54.48/54.87 Deleted: 1230
% 54.48/54.87 Deletedinuse: 17
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying clauses:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 304517
% 54.48/54.87 Kept: 82898
% 54.48/54.87 Inuse: 1454
% 54.48/54.87 Deleted: 1630
% 54.48/54.87 Deletedinuse: 17
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 314370
% 54.48/54.87 Kept: 85060
% 54.48/54.87 Inuse: 1488
% 54.48/54.87 Deleted: 1630
% 54.48/54.87 Deletedinuse: 17
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 324043
% 54.48/54.87 Kept: 87269
% 54.48/54.87 Inuse: 1518
% 54.48/54.87 Deleted: 1630
% 54.48/54.87 Deletedinuse: 17
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 333316
% 54.48/54.87 Kept: 89399
% 54.48/54.87 Inuse: 1548
% 54.48/54.87 Deleted: 1630
% 54.48/54.87 Deletedinuse: 17
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 353388
% 54.48/54.87 Kept: 94669
% 54.48/54.87 Inuse: 1573
% 54.48/54.87 Deleted: 1631
% 54.48/54.87 Deletedinuse: 18
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 367228
% 54.48/54.87 Kept: 101548
% 54.48/54.87 Inuse: 1578
% 54.48/54.87 Deleted: 1631
% 54.48/54.87 Deletedinuse: 18
% 54.48/54.87
% 54.48/54.87 Resimplifying inuse:
% 54.48/54.87 Done
% 54.48/54.87
% 54.48/54.87
% 54.48/54.87 Intermediate Status:
% 54.48/54.87 Generated: 380138
% 54.48/54.87 Kept: 105195
% 54.48/54.87 Inuse: 1583
% 110.52/110.93 Deleted: 1631
% 110.52/110.93 Deletedinuse: 18
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93 Resimplifying clauses:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93
% 110.52/110.93 Intermediate Status:
% 110.52/110.93 Generated: 407877
% 110.52/110.93 Kept: 110997
% 110.52/110.93 Inuse: 1598
% 110.52/110.93 Deleted: 1866
% 110.52/110.93 Deletedinuse: 18
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93
% 110.52/110.93 Intermediate Status:
% 110.52/110.93 Generated: 417761
% 110.52/110.93 Kept: 113008
% 110.52/110.93 Inuse: 1624
% 110.52/110.93 Deleted: 1866
% 110.52/110.93 Deletedinuse: 18
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93
% 110.52/110.93 Intermediate Status:
% 110.52/110.93 Generated: 427373
% 110.52/110.93 Kept: 115223
% 110.52/110.93 Inuse: 1653
% 110.52/110.93 Deleted: 1866
% 110.52/110.93 Deletedinuse: 18
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93
% 110.52/110.93 Intermediate Status:
% 110.52/110.93 Generated: 437165
% 110.52/110.93 Kept: 117301
% 110.52/110.93 Inuse: 1673
% 110.52/110.93 Deleted: 1866
% 110.52/110.93 Deletedinuse: 18
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93
% 110.52/110.93 Intermediate Status:
% 110.52/110.93 Generated: 449337
% 110.52/110.93 Kept: 119412
% 110.52/110.93 Inuse: 1703
% 110.52/110.93 Deleted: 1866
% 110.52/110.93 Deletedinuse: 18
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93
% 110.52/110.93 Intermediate Status:
% 110.52/110.93 Generated: 458739
% 110.52/110.93 Kept: 121980
% 110.52/110.93 Inuse: 1728
% 110.52/110.93 Deleted: 1866
% 110.52/110.93 Deletedinuse: 18
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93
% 110.52/110.93 Intermediate Status:
% 110.52/110.93 Generated: 468072
% 110.52/110.93 Kept: 124112
% 110.52/110.93 Inuse: 1758
% 110.52/110.93 Deleted: 1866
% 110.52/110.93 Deletedinuse: 18
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93 Resimplifying clauses:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93
% 110.52/110.93 Intermediate Status:
% 110.52/110.93 Generated: 482926
% 110.52/110.93 Kept: 127676
% 110.52/110.93 Inuse: 1778
% 110.52/110.93 Deleted: 2085
% 110.52/110.93 Deletedinuse: 18
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93
% 110.52/110.93 Intermediate Status:
% 110.52/110.93 Generated: 492727
% 110.52/110.93 Kept: 129809
% 110.52/110.93 Inuse: 1783
% 110.52/110.93 Deleted: 2085
% 110.52/110.93 Deletedinuse: 18
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93
% 110.52/110.93 Intermediate Status:
% 110.52/110.93 Generated: 500355
% 110.52/110.93 Kept: 132076
% 110.52/110.93 Inuse: 1806
% 110.52/110.93 Deleted: 2087
% 110.52/110.93 Deletedinuse: 18
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93
% 110.52/110.93 Intermediate Status:
% 110.52/110.93 Generated: 510676
% 110.52/110.93 Kept: 135936
% 110.52/110.93 Inuse: 1818
% 110.52/110.93 Deleted: 2088
% 110.52/110.93 Deletedinuse: 19
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93 Resimplifying inuse:
% 110.52/110.93 Done
% 110.52/110.93
% 110.52/110.93
% 110.52/110.93 Intermediate Status:
% 110.52/110.93 Generated: 518075
% 110.52/110.93 Kept: 137958
% 110.52/110.94 Inuse: 1842
% 110.52/110.94 Deleted: 2088
% 110.52/110.94 Deletedinuse: 19
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94
% 110.52/110.94 Intermediate Status:
% 110.52/110.94 Generated: 527072
% 110.52/110.94 Kept: 139976
% 110.52/110.94 Inuse: 1862
% 110.52/110.94 Deleted: 2088
% 110.52/110.94 Deletedinuse: 19
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94
% 110.52/110.94 Intermediate Status:
% 110.52/110.94 Generated: 535512
% 110.52/110.94 Kept: 142200
% 110.52/110.94 Inuse: 1886
% 110.52/110.94 Deleted: 2088
% 110.52/110.94 Deletedinuse: 19
% 110.52/110.94
% 110.52/110.94
% 110.52/110.94 Intermediate Status:
% 110.52/110.94 Generated: 570686
% 110.52/110.94 Kept: 148268
% 110.52/110.94 Inuse: 1896
% 110.52/110.94 Deleted: 2088
% 110.52/110.94 Deletedinuse: 19
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94 Resimplifying clauses:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94
% 110.52/110.94 Intermediate Status:
% 110.52/110.94 Generated: 578674
% 110.52/110.94 Kept: 150298
% 110.52/110.94 Inuse: 1924
% 110.52/110.94 Deleted: 2304
% 110.52/110.94 Deletedinuse: 19
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94
% 110.52/110.94 Intermediate Status:
% 110.52/110.94 Generated: 587062
% 110.52/110.94 Kept: 152917
% 110.52/110.94 Inuse: 1946
% 110.52/110.94 Deleted: 2304
% 110.52/110.94 Deletedinuse: 19
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94
% 110.52/110.94 Intermediate Status:
% 110.52/110.94 Generated: 592861
% 110.52/110.94 Kept: 154951
% 110.52/110.94 Inuse: 1962
% 110.52/110.94 Deleted: 2305
% 110.52/110.94 Deletedinuse: 20
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94
% 110.52/110.94 Intermediate Status:
% 110.52/110.94 Generated: 598350
% 110.52/110.94 Kept: 157286
% 110.52/110.94 Inuse: 1971
% 110.52/110.94 Deleted: 2305
% 110.52/110.94 Deletedinuse: 20
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94
% 110.52/110.94 Intermediate Status:
% 110.52/110.94 Generated: 604109
% 110.52/110.94 Kept: 159573
% 110.52/110.94 Inuse: 1981
% 110.52/110.94 Deleted: 2305
% 110.52/110.94 Deletedinuse: 20
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94
% 110.52/110.94 Intermediate Status:
% 110.52/110.94 Generated: 610398
% 110.52/110.94 Kept: 161878
% 110.52/110.94 Inuse: 1996
% 110.52/110.94 Deleted: 2305
% 110.52/110.94 Deletedinuse: 20
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94
% 110.52/110.94 Intermediate Status:
% 110.52/110.94 Generated: 616081
% 110.52/110.94 Kept: 164216
% 110.52/110.94 Inuse: 2006
% 110.52/110.94 Deleted: 2305
% 110.52/110.94 Deletedinuse: 20
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94
% 110.52/110.94 Intermediate Status:
% 110.52/110.94 Generated: 622172
% 110.52/110.94 Kept: 166221
% 110.52/110.94 Inuse: 2022
% 110.52/110.94 Deleted: 2305
% 110.52/110.94 Deletedinuse: 20
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94 Resimplifying inuse:
% 110.52/110.94 Done
% 110.52/110.94
% 110.52/110.94
% 110.52/110.94 Intermediate Status:
% 110.52/110.94 Generated: 631607
% 110.52/110.94 Kept: 168463
% 110.52/110.94 Inuse: 2046
% 218.51/219.10 Deleted: 2305
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying clauses:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 641444
% 218.51/219.10 Kept: 171729
% 218.51/219.10 Inuse: 2061
% 218.51/219.10 Deleted: 3180
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 648558
% 218.51/219.10 Kept: 174758
% 218.51/219.10 Inuse: 2071
% 218.51/219.10 Deleted: 3180
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 656454
% 218.51/219.10 Kept: 176763
% 218.51/219.10 Inuse: 2088
% 218.51/219.10 Deleted: 3180
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 662897
% 218.51/219.10 Kept: 178779
% 218.51/219.10 Inuse: 2102
% 218.51/219.10 Deleted: 3180
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 672069
% 218.51/219.10 Kept: 181208
% 218.51/219.10 Inuse: 2116
% 218.51/219.10 Deleted: 3180
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 682183
% 218.51/219.10 Kept: 183931
% 218.51/219.10 Inuse: 2131
% 218.51/219.10 Deleted: 3180
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 691764
% 218.51/219.10 Kept: 186391
% 218.51/219.10 Inuse: 2146
% 218.51/219.10 Deleted: 3180
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 701066
% 218.51/219.10 Kept: 189367
% 218.51/219.10 Inuse: 2161
% 218.51/219.10 Deleted: 3180
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying clauses:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 709838
% 218.51/219.10 Kept: 191442
% 218.51/219.10 Inuse: 2181
% 218.51/219.10 Deleted: 3356
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 721200
% 218.51/219.10 Kept: 193685
% 218.51/219.10 Inuse: 2216
% 218.51/219.10 Deleted: 3356
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 729248
% 218.51/219.10 Kept: 195733
% 218.51/219.10 Inuse: 2236
% 218.51/219.10 Deleted: 3356
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 737496
% 218.51/219.10 Kept: 197992
% 218.51/219.10 Inuse: 2251
% 218.51/219.10 Deleted: 3356
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 754581
% 218.51/219.10 Kept: 201871
% 218.51/219.10 Inuse: 2271
% 218.51/219.10 Deleted: 3356
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 765104
% 218.51/219.10 Kept: 204071
% 218.51/219.10 Inuse: 2301
% 218.51/219.10 Deleted: 3356
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 775663
% 218.51/219.10 Kept: 206702
% 218.51/219.10 Inuse: 2306
% 218.51/219.10 Deleted: 3356
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 793454
% 218.51/219.10 Kept: 211027
% 218.51/219.10 Inuse: 2331
% 218.51/219.10 Deleted: 3356
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying clauses:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 800945
% 218.51/219.10 Kept: 213185
% 218.51/219.10 Inuse: 2346
% 218.51/219.10 Deleted: 3663
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 810984
% 218.51/219.10 Kept: 215206
% 218.51/219.10 Inuse: 2376
% 218.51/219.10 Deleted: 3663
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 819568
% 218.51/219.10 Kept: 217207
% 218.51/219.10 Inuse: 2401
% 218.51/219.10 Deleted: 3663
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 830054
% 218.51/219.10 Kept: 219209
% 218.51/219.10 Inuse: 2427
% 218.51/219.10 Deleted: 3663
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 838124
% 218.51/219.10 Kept: 221542
% 218.51/219.10 Inuse: 2446
% 218.51/219.10 Deleted: 3663
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 846521
% 218.51/219.10 Kept: 223964
% 218.51/219.10 Inuse: 2464
% 218.51/219.10 Deleted: 3665
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 857366
% 218.51/219.10 Kept: 226234
% 218.51/219.10 Inuse: 2484
% 218.51/219.10 Deleted: 3665
% 218.51/219.10 Deletedinuse: 20
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10 Resimplifying inuse:
% 218.51/219.10 Done
% 218.51/219.10
% 218.51/219.10
% 218.51/219.10 Intermediate Status:
% 218.51/219.10 Generated: 866Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------